Wild Mushroom Quesadillas with Warm Black Bean Salsa

Name: Wild Mushroom Quesadillas with Warm Black Bean Salsa
Ingredients: 2 tablespoons extra-virgin olive oil, 2 turns of the pan, plus some for drizzling; 16 crimini mushroom caps, baby portobellos, with stems, trimmed and thinly sliced; 12 shiitake mushrooms, thinly sliced, stems discarded; Coarse black pepper and salt; 1 tablespoon (a few sprigs) fresh thyme leaves, chopped, or 1 teaspoon dried; 4 large flour tortillas, 12 inches in diameter; 2 cups shredded sharp white cheddar; 1 tablespoon extra-virgin olive oil, 1 turn of the pan; 1 small onion, chopped; 2 cloves garlic, chopped; 1 jalapeno pepper, seeded and chopped; 1 can black beans, drained; 1 cup frozen corn kernels; 1/2 cup sun-dried tomatoes in oil, chopped; 1/2 cup smoky barbecue sauce; Salt and freshly ground black pepper