In a medium bowl, add prepared mushrooms, onions, garlic and chilies. Toss to mix well.
Place oil in a large heavy skillet. Place skillet over medium-high heat.
When oil is hot and shimmering add mushroom mixture.
Season very lightly with salt and pepper.
Cook, stirring and tossing, until mushrooms are browned, 6 to 10 minutes. Scrape into a bowl.
Taste. Add salt and pepper, to taste, if needed.
Divide cheese equally among all 6 tortillas, spreading a portion over half of each tortilla. Leave a small empty border, about 1 inch, at the edge.
Spoon mushroom mixture on top of cheese, evenly among the tortillas.
Divide the epazote leaves, if using, among the tortillas.
Fold the empty side over the filling. Press firmly to close.
Heat a cast-iron or other heavy griddle over medium heat.
Place a tortilla, or 2 tortillas, if they will fit, into the hot pan. Cook, turning once, until light golden brown and crisp, about 3 minutes per side.
Remove from heat to a serving plate. Cut into 3 or 4 wedges.
Repeat until all quesadillas are cooked.
Serve immediately, with sour cream and salsa verde on the side. (See Box below for a recipe for Moe's Southwest Grill Salsa Verde)