Place 1 tablespoon butter in a medium skillet. Place over medium heat. When butter has melted and is hot (do not burn), add onions. Sauté until they just begin to brown.
Stir in garlic. Cook until aroma is released, about 1 minute longer.
Add mushrooms, salt, pepper and arbol chiles. Continue cooking until mushrooms soften and excess juice evaporates, about 5 to 10 minutes.
Stir in epazote or parsley. Briefly cook just to release its flavor, about a minute.
Remove skillet from heat and set aside to cool.
In a large bowl, combine all 3 cheeses. Mix well.
Lay tortillas out on a counter, cutting board or other work surface.
Divide cheese mixture into 2 portions. Arrange 1 portion over 1/2 of each tortilla.
Divide mushroom mixture into 2 portions. Sprinkle 1 portion over evenly over each cheese.
Fold over each tortilla to enclose filling.
Place remaining butter in a large skillet. When butter is hot, place 2 folded quesadillas in pan.
Cook until very light golden, about 1 minute, then flip over.
Cook until other side is golden and cheese begins to ooze.
Serve hot, whole or cut into wedges.