Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms and garlic. Cook 5 to 7 minutes or until mushrooms are browned and liquid is evaporated, stirring often. Stir in onion, tomato, cilantro, TABASCO® Green Sauce, and salt and cook 1 minute longer; remove from heat and set aside.
Combine cheeses and sprinkle 2 tablespoons evenly over each of 4 tortillas; place another tortilla on top of each tortilla with cheese and top each with an additional 2 tablespoons cheese and 2 tablespoons mushroom filling.
Place quesadillas on a greased baking sheet and bake in a 400° oven for 4 to 5 minutes or until cheese is melted. Cut in quarters and serve immediately.
Makes 16 appetizer servings.