Step 1

To make the mushroom filling: Heat the oil and butter in a large skillet over medium-high heat until the butter melts and starts to foam. Add the onion and cook until soft and translucent, 3 to 4 minutes. Add the chile and cook until softened, 1 to 2 minutes. Add the garlic and cook until just fragrant, less than a minute; do not let it brown. Add the mushrooms and salt and cook, stirring occasionally, until the mushrooms release their juices and the liquid begins to evaporate, about 5 minutes. Add the epazote and cook for 1 minute, or until the mushrooms are just slightly moist, neither wet nor dry. Remove from the heat.

Step 2

If making homemade tortillas: Cut two circles about the size of the tortilla press plates (or at least 6 inches in diameter if using a rolling pin) out of thin plastic bags, such as produce bags from the grocery store.

Step 3

In a large bowl, mix the masa flour with the water and knead for a couple of minutes, until soft. Roll a piece of the dough in the palm of your hand into a ball about 1 inch in diameter. Place one of the plastic circles on the bottom of the tortilla press and place the ball on top. Place the other plastic circle on top of the ball and clamp down on the press to make a flat disk about ¼ inch thick, jiggling the press a little as you get to the bottom (this makes for a rounder tortilla). (Alternatively, you can place the ball between plastic sheets or parchment paper and roll the tortillas out with a rolling pin into 5-inch-diameter circles.)

Step 4

Remove the top piece of plastic and place a generous 2 tablespoons of the cheese and about 1½ tablespoons of the mushroom filling in the center of the dough. Use the bottom piece of plastic to fold the tortilla over the filling like a turnover. Firmly pinch the edges of the turnover together. Gently lift the quesadilla off the plastic and set aside. Continue with the remainder of the dough, cheese, and mushroom filling.

Step 5

Heat 1 inch of oil in a 12-inch skillet over medium heat until hot but not smoking. The oil is ready if when you dip the edge of a quesadilla into the oil, it bubbles happily all around it without going wild. Add the quesadillas a few at a time, making sure not to crowd the skillet, and cook for 2 to 4 minutes per side, or until golden brown and lightly crisp. With a slotted spoon, transfer to a paper-towel-lined platter to drain. Keep warm while you repeat with the remaining quesadillas.

Step 6

If using store-bought tortillas: Heat a comal, a flat griddle, or a 12-inch skillet over medium heat for 8 to 10 minutes, or until thoroughly heated. (If the pan isn’t hot enough, the tortillas will stick to it.) Lay a tortilla on the comal and heat for about 20 seconds on each side, until it softens and becomes pliable. Add about 2 tablespoons cheese and about 1½ tablespoons of filling in the center of the tortilla. Fold the tortilla over, press down lightly, and let cook until the cheese has melted and the tortilla has begun to crisp lightly, 2 to 3 minutes. Turn and continue cooking until the second side begins to crisp lightly, another 2 to 3 minutes. Transfer to a platter, cover to keep warm, and repeat with the remaining tortillas, cheese, and filling.

Step 7

Serve the quesadillas hot, with the salsa.