During late August and early September in New Mexico, the air is filled with the pungent aroma of roasting green chilies. Just the thought of it makes me nostalgic for the years when I lived in Santa Fe.

For if there is one ingredient necessary for traditional New Mexican cooking, it is the long, spicy, local green chili. Well, and also its ruddy twin, the dried red chili. It’s exactly the same chili, allowed to ripen completely and turn bright red. Red chilies are braided into the garlands called ristras, which are hung up to dry for later use.

But back to the green. Most people there buy their green chilies in quantity, by the bag or the bushel, and then stand in line waiting their turn to have them roasted by seasonal professionals who set up in parking lots or roadside stands. The freshly picked chilies are tossed into a roaster — essentially a perforated metal drum rigged to spin over a powerful flame just long enough to blister the skins. The heat cooks the chilies a bit in the process.

Once you get your roasted chilies home, the modern tradition is to make up small packages in zippered plastic bags and store them in the freezer, taking out a couple of bags to thaw as necessary. Some people peel and seed them before freezing; others opt to perform that chore afterward. It can seem less daunting doing one bag at a time. With a good supply on hand you’ll be able to make green chili sauce, green chili stew, green chili enchiladas, even green chili cheeseburgers, whenever you wish.

The most famous (and some say the most desirable) green chilies are known as Hatch chilies, grown in the southern part of the state. Like Champagne, which can only be called Champagne if it is grown in the Champagne region of France, a true Hatch chili can only come from the Hatch Valley. Beware of mislabeled counterfeits.

But there are perfectly good green chilies grown outside that specific region. You can search the Internet for companies that ship Hatch chilies, both fresh and frozen. If you can’t find the real deal, look for the widely available Anaheim chili, developed in California, which makes a pretty good substitute. Just roast them under the broiler or over hot coals for a small batch. When cool, scrape away skins and seeds with a paring knife.

Try this recipe for a basic green chili sauce. It will add a New Mexican kick to nearly anything, but it is especially nice spooned liberally over a hearty breakfast quesadilla.

GREEN CHILI BREAKFAST QUESADILLAS

Time: 1 hour

Yield: 4 servings

For the green chili sauce

2 Tbsp. butter, lard or vegetable oil

1 small onion, finely diced

Kosher salt

4 garlic cloves, minced

2 Tbsp. all-purpose flour

2 cups chicken broth or water

2 cups chopped Hatch or Anaheim green chilies (roasted, peeled and seeded), from about 2 pounds chilies

1/2 tsp. cumin seeds, toasted and coarsely ground

1/2 tsp. oregano

For the quesadillas

4 large flour tortillas, plain or whole wheat

8 oz. grated cheese, such as Oaxaca string cheese or Monterey Jack

2 Tbsp. butter

2 medium-size cooked peeled potatoes, cut in small cubes, about 1 1/2 cups (optional)

6 to 8 eggs, lightly beaten

Salt and pepper

4 oz. queso fresco or cotija cheese, crumbled

Handful of cilantro sprigs

1 firm-ripe avocado, sliced

Radishes, optional, for garnish

Make the green chili sauce: Put butter in a heavy-bottomed saucepan over medium heat. Add onion, season lightly with salt and cook, stirring, until softened but not browned, about 5 minutes. Add garlic and cook for 1 minute more. Sprinkle in flour and stir to coat.

Add broth a little at a time, whisking constantly until thickened, about 2 minutes. Add chopped chili, cumin, oregano and about 1/2 teaspoon salt. Lower heat and simmer, stirring occasionally, for 15 to 20 minutes. You should have about 3 cups medium-thick sauce. (May be prepared in advance and refrigerated for up to 5 days.) Keep sauce warm.

Make the quesadillas: Heat oven to 350 degrees. Set a large cast-iron skillet over medium-high heat. Warm tortillas on both sides, one at a time, without allowing them to crisp or brown much. Place tortillas on a baking sheet (you may need 2) and sprinkle each with 2 ounces of the grated cheese. Put in oven to melt cheese.

Melt butter in a small skillet over medium heat. Add potatoes if using, heat them through and let lightly brown. Season eggs with salt and pepper, pour over potatoes and quickly stir mixture until eggs are soft-scrambled. Remove tortillas from oven and place 1/4 of the cooked egg mixture at the center of each. Fold tortillas in half and transfer to 4 warm plates. Spoon 1/4 cup warm green chili sauce over each quesadilla. Sprinkle with queso fresco and top with cilantro sprigs and avocado slices. Garnish with whole or halved radishes if desired. Serve immediately.