These quesadillas are cooked on the grill. Serve them with salsa and sour cream.
Serves 12 to 16.
Melt butter in large skillet over medium-high heat. Add chili powder, garlic and oregano. Sauté until fragrant, about 1 minute. Add shiitake and button mushrooms and sauté until tender, about 10 minutes. Remove from heat. Mix in chicken, onion and cilantro. Cool 10 minutes. Mix in cheese. Season with salt and pepper. (Can be made 8 hours ahead. Cover and chill.)
Prepare barbecue (medium heat). Lightly brush oil on 1 side of 8 tortillas. Place tortillas, oil side down, on large baking sheet. Divide chicken mixture among tortillas, spreading to even thickness. Top with remaining 8 tortillas; press, then brush with oil.Grill quesadillas until heated through and golden brown, about 3 minutes per side. Cut into wedges.