2 tablespoons extra virgin olive oil (EVOO), plus some for drizzling
16 crimini mushroom caps or baby portobellos, with stems, trimmed and thinly sliced
12 shiitake mushrooms, stems discarded, thinly sliced
Coarse black pepper and salt
1 tablespoon fresh thyme leaves (a few sprigs), chopped, or 1 teaspoon dried thyme
4 large flour tortillas (12-inch)
2 cups sharp white cheddar, shredded
1 tablespoon extra virgin olive oil (EVOO)
1 small onion, chopped
2 cloves garlic, chopped
1 jalapeño pepper, seeded and chopped
1 can black beans, drained
1 cup frozen corn kernels
1/2 cup sundried tomatoes in oil, chopped
1/2 cup smoky barbecue sauce
Salt and freshly ground black pepper
Heat a medium nonstick skillet over medium heat. Add the EVOO, two turns of the pan, and the sliced mushrooms to the hot skillet. Season mushrooms with black pepper, salt and thyme. Sauté the mushrooms 10 minutes, or until dark and tender, then remove from heat. Transfer the mushrooms to a dish and return the skillet to the stove over medium heat.
Add another turn of EVOO to the skillet and add the onions, garlic and jalapeño pepper; sauté for 2-3 minutes, then add beans and corn to the pan. Stir in chopped tomatoes and barbecue sauce, then season salsa with salt and pepper. Transfer warm salsa to a serving dish.
Heat a griddle pan or large nonstick skillet over medium to medium-high heat. Add a drizzle of EVOO to the pan and one flour tortilla. Cook tortilla 1 minute, then turn it over. Sprinkle 1/2 cup sharp cheddar over half of the flour tortilla. Cover the cheese with a quarter of the cooked sliced mushrooms. Fold the plain half of the tortilla over top of the filling and gently press down with a spatula. Cook the filled quesadilla 30-60 seconds longer on each side to lightly brown and crisp the quesadilla and melt the cheese. Remove the quesadilla to a large cutting board or transfer to a warm oven to hold, then repeat with remaining quesadilla ingredients.
Cut each quesadilla into wedges and serve with warm salsa for topping.