Because the cream cheese and asparagus release a fair amount of moisture when they cook (and they don’t need much time in the oven), it’s best to par-bake the crust. To save time, you can pop the crust in the oven while you prepare the cheese mixture and trim the asparagus. Once the crust just starts to puff and turn golden brown, pull it from the oven and very carefully top it with the cheese and asparagus. At that point, add most of the thyme so that it softens and melds with the crust. Saving a few pinches for serving brings greater complexity to the dish.
I like to add a final drizzle of the best olive oil I’ve got on hand, plus a sprinkle of flaky salt, right before serving with a simple mixed green salad.