Who needs a recipe for a quesadilla? Grab a flour tortilla, pile on shredded cheese and heat it up in a pan until the cheese melts. There, I summed up about 75 percent of the quesadilla recipes around, and you only had to read one sentence. Of course, you could add some chicken, which would account for another 10 percent of the recipes, but that’s stretching the limit of most people’s quesadilla comprehension.

There’s absolutely nothing wrong with this kind of quesadilla. Gooey, melted cheese on a tortilla is almost always a fine and good thing, but it’s not the only quesadilla available. In fact, it’s helpful to think of quesadillas in two broad categories: those made with pre-made tortillas and those made with fresh masa.

The latter, especially, are less vehicles strictly for cheese consumption and more like empanadas or turnovers. In “Authentic Mexican,” Rick Bayless describes them as “deliciously stuffed pockets of Mexican flavor, bearers of well-spiced vegetables, meats and cheese, transporters of chile-spiked hot sauce or smooth guacamole,” which sums it up nicely. Notice how cheese isn’t the sole ingredient?

In fact, numerous recipes exist for quesadillas made with fresh masa in which cheese plays a limited or, in some rare cases, completely nonexistent role. In “My Mexico,” Diana Kennedy offers a number of quesadilla recipes in which the only cheese is some crumbled queso fresco sprinkled on top. Dudley Nieto and Bruce Kraig’s “Cuisines of Hidden Mexico” includes a recipe for quesadillas de huitlacoche (the prized black corn fungus) with no cheese whatsoever.

How can a quesadilla exist without cheese? Honestly, you’d be forgiven for thinking of these as a kind of empanada. Though, there’s a chance we’re thinking about this too much. In their rambunctiously entertaining “Tacopedia,” Juan Carlos Mena and Deborah Holtz delve into the paradox of “cheeseless quesadillas,” noting that while it doesn’t exactly make a lot of sense, “that’s their name, so what can we do?” Good point.

Regardless of whether they have cheese or not, these kinds of quesadillas are mostly made with fresh masa, the same corn dough that’s used to make corn tortillas. Occasionally other ingredients, like lard, wheat flour and baking soda are added to the masa, though not always. The masa dough is flattened into a circle using a tortilla press, a small amount of the filling is added across the middle and then the masa is folded up to form a half-moon shape. This is griddled or gently fried until it develops a golden-browned crust, ever so slightly crackly without being crisp.

There are a bewildering collection of variations for these kinds of quesadilla. Though rajas (charred strips of poblano) and huitlacoche (a black corn fungus) are very common, essentially any filling you could have in a taco can make the transition to quesadilla. The only rule is moderation. Add too much cheese or filling, and the dough will crack, unleashing the innards all over the skillet. Certain additions also change the name. The sincronizada often features ham in the mix, while gringas demand al pastor meat. These would both still be considered quesadilla variations.

It’s tempting to crown quesadillas made with fresh masa as the pinnacle of the quesadilla-making arts. If you haven’t experienced them, I’d suggest you give them a try. But it’s important to know that there’s no shame in using pre-made tortillas for quesadillas, as long as you treat them with the slightest bit of care.

Unlike quesadillas made with fresh masa, folded-over quesadillas basically require cheese. Forget, forever if you can, the pre-shredded “Mexican cheese” found in the supermarket. What you want is something tangy that melts easily. This can be as simple as a decent quality Monterrey Jack, or, if you’re near a well-stocked Mexican grocery store, Chihuahua or Oaxacan cheese is deal.

While store-bought corn tortillas make fine quesadillas, especially if you add some fat to the skillet when crisping them, I do actually prefer the flakiness of flour tortillas here. When cooked in a little fat, the flour tortillas develop a gorgeous speckled browned appearance and hold the fillings without cracking.

The extra strength of flour tortillas also allows us to be slightly more liberal with the amount of filling. That means that you can add multiple components, just so long as you’re smart about it. Let’s tackle the most common meat-filled one out there: the chicken quesadilla.

The problem with most chicken quesadillas is that the meat and the cheese never join forces. Instead, the meat usually falls off after a few bites. The key to fixing this is use shredded chicken meat, instead of hulking grilled slices. Leftover roast chicken is great here.

I also like to add something acidic to help cut through the heaviness. That can be as simple as adding some canned pickled jalapeno slices, but if you have an hour, you can easily make quick-pickled jalapenos and red onions, which add an appealing freshness to each bite.

The only crime here is unmelted cheese. Cook over too high of heat and the outside of the tortilla burns before the cheese has time to melt, so make sure to cook over a steady medium, flipping the quesadilla occasionally to prevent the tortilla from burning.

Don’t be afraid to get creative. Quesadillas thrive on innovation. Ever tried kimchi quesadillas, which were popularized by Los Angeles chef Roy Choi and his Kogi Truck? Sounds crazy, but the spicy pickled heat of the fermented cabbage works extremely well against a pile of gooey cheese. Honestly, my family often has quesadilla night when we need to use up leftovers. Nothing like thrift to lead you down unexpectedly delicious directions.

Quesadillas with Fresh Corn Masa

Prep: 35 minutes

Cook: 20 minutes

Makes: 8 quesadillas

Look for fresh masa dough at tortilla factories or Mexican grocery stores, or use masa flour for tortillas and follow the directions on the package to make the dough.

2 poblano chiles

2 tablespoons canola oil, divided

1 large white onion, cut into 1/4-inch thick slices

1/2 teaspoon salt

1 clove garlic, minced

1/2 cup chopped fresh epazote (if available) or fresh cilantro

12 ounces fresh masa dough

1/2 pound shredded Monterey Jack or queso Chihuahua

Guacamole for serving

1. If using a gas stove: Place poblano chiles on the grate above a burner. Turn heat to high. Cook until blackened on the bottom. Use a pair of tongs to rotate the chiles until blackened all over. Transfer chiles to a paper bag to steam, 15 minutes. Peel off blackened skin, and remove stems and seeds. Cut poblanos into 1/4-inch thick slices.

2. If using a broiler: Adjust oven rack to top, and heat broiler to high. Set chiles on a foil-lined baking sheet, and slide sheet underneath the broiler. Cook until blackened on top, 3 to 4 minutes. Flip and cook until blackened on the other side, another 3 to 4 minutes. Transfer chiles to a plastic bag to steam for 15 minutes. Peel off blackened skin, and remove stems and seeds. Cut poblanos into 1/4-inch thick strips.

3. Heat 1 tablespoon of oil in a large skillet over medium-high heat. Add poblano and onion slices; season with salt. Cook, stirring often, until onions are lightly browned, 8 to 10 minutes. Add garlic and epazote (or cilantro), and stir well. Cook until garlic is fragrant, about 30 seconds. Turn off heat. Transfer chile and onion mixture to a bowl; set aside until cool. Clean out the skillet.

4. Heat remaining tablespoon of oil in the skillet over medium heat.

5. Divide masa into 1 1/2-ounce balls (about the size of a pingpong ball). Place an 8-inch round sheet of plastic (thin grocery store bags work extremely well) on the bottom plate of a tortilla press. Set one masa ball on the plastic, and place a second 8-inch round sheet of plastic on top. Flatten the masa gently with the tortilla press, until it’s about a 4-inch circle and about 1/16-inch thick. You may need to press more than once for an even quesadilla, turning the disk 90 degrees between each pressing.

6. Carefully remove the top sheet of plastic. Place an ounce of cheese and a few strips of the poblano and onion on half of the masa circle. Using the bottom plastic sheet, fold the quesadilla in half to form a half moon shape. Compress the edges, so that no filling can get out. Gently roll the quesadilla onto your hand; transfer directly to the skillet. Cook, flipping the quesadilla every minute or so, until the exterior is nicely browned, 6 to 8 minutes. Repeat with remaining masa balls. Serve with guacamole.

Nutrition information per quesadilla: 293 calories, 14 g fat, 6 g saturated fat, 25 mg cholesterol, 33 g carbohydrates, 1 g sugar, 12 g protein, 317 mg sodium, 3 g fiber

Chicken Quesadillas with Pickled Red Onion and Jalapenos

Prep: 25 minutes

Cook: 4-6 minutes per batch

Makes: 4 quesadillas

1 cup apple cider vinegar

2 teaspoons salt

2 tablespoon sugar

1/2 red onion, thinly sliced

2 jalapenos, thinly sliced

8 ounces shredded Monterey Jack or queso Chihuahua

4 ounces cooked, shredded chicken breast

4 (8-inch) flour tortillas

1 tablespoon canola oil

Guacamole or salsa

1. Pour apple cider vinegar into a medium bowl. Add salt and sugar; stir until dissolved. Add red onion and jalapenos. Set aside for an hour. Drain before using.

2. Place a quarter of the shredded cheese and shredded chicken on half of a tortilla. Add pickled red onion and jalapeno slices to taste. Fold in half. Repeat with remaining tortillas.

3. Heat oil in a large skillet over medium heat. Place two of the quesadillas in the pan. Cook, 2 minutes per side. Repeat with other two quesadillas. Cut into triangles and serve with guacamole.

Nutrition information per quesadilla: 450 calories, 27 g fat, 13 g saturated fat, 74 mg cholesterol, 28 g carbohydrates, 3 g sugar, 25 g protein, 1,048 mg sodium, 1 g fiber