How to Make It
In a large skillet, melt 1 tablespoon of the butter over moderately high heat. Add the mushrooms, season with salt and pepper and cook until they begin to brown, 6 to 7 minutes.
In a food processor, pulse the zucchini until minced. Add the spinach and process until minced.
In a large saucepan, melt 1 tablespoon of the butter in the olive oil over moderate heat. Add the onion, garlic, jalapeños and oregano and cook, stirring frequently, until the onion is softened but not browned, about 8 minutes. Add the zucchini mixture and the olives and cook, stirring often, until the mixture is hot and any liquid has evaporated, about 5 minutes. Season with salt. Remove from the heat and let cool for 5 minutes, then stir in the cotija and mozzarella cheeses.
Lay 4 of the tortillas on a work surface and top them with the vegetable filling and the cooked mushrooms. Top with the remaining tortillas and press together lightly with your hands to form the quesadillas.
Set a large skillet over moderately high heat. Add 1/2 tablespoon of the butter and 1 of the quesadillas and cook until golden brown, about 2 minutes. Flip the quesadilla, adding another 1/2 tablespoon of the butter to the skillet. Cook until golden, another 1 to 2 minutes. Repeat with the remaining butter and quesadillas. Quarter the quesadillas and serve them with sour cream.
Cotija cheese is a dry, crumbly cheese that adds a salty, pungent flavor to all kinds of Mexican dishes. It is available at Latin food markets, but feta cheese makes a fine substitute.