Heat the oil over medium heat in a large, heavy frying pan. Add the onions and cook, stirring, until translucent, about 5 minutes. Add the mushrooms and chiles and continue cooking until golden brown, about 5 more minutes. Season with salt and pepper. Add the cilantro and set aside.
For the blue corn tortillas:
In a bowl, mix the harina de maiz azul, masa harina and salt with the warm water using a wooden spoon until a dough is formed, about 2 minutes. Let stand, covered tightly with plastic wrap, for 2 minutes.
Divide the dough into 12 parts. Roll each part into a ball, keeping the balls you are not using in a plastic bag so that they don't dry out. (If the dough does get too dry, add a little extra water.).
Place a ball on a sheet of plastic wrap and cover it with another sheet. Flatten slightly with the palm of your hand, and then finish rolling with a rolling pin, working quickly and lightly. Flip the package over and repeat until an approximately 6-inch circle is formed. Repeat with all the dough balls.
Preheat a flat griddle or pan to high heat.
Peel away the top layer of plastic wrap, flip the package over gently and peel away the other piece of plastic wrap. Transfer to the griddle.
Bake on the first side for about 30 seconds. Flip and bake on the second side for about 30 seconds. Flip once again. Remove from the griddle and keep warm.
To assemble, spread with a quarter of the cheese on 1 tortilla. Garnish with a quarter of the mushrooms and top with another tortilla. Place on the griddle, turn the heat down to medium-high and press down gently. Cook until the cheese begins to melt. Flip the quesadilla, and heat for another minute. Repeat with the remaining ingredients. Serve with salsa if desired.
Queso fresco is a fresh Mexican cheese. You can substitute with a soft goat cheese or fresh ricotta.
Epazote is a Mexican herb that resembles tarragon.