Heat butter, 1 tablespoon of the oil, and TABASCO® Sauce in a large skillet over medium-high heat until butter melts. Add pepper strips, salt, and pepper and cook until softened and lightly browned, about 12 minutes. Set aside. Combine cheeses in a large bowl.
Heat a nonstick skillet over medium heat. Brush one side of a tortilla with oil and place oil side down in skillet. Sprinkle tortilla with 1/3 cup cheese mixture and 1/3 cup pepper mixture. Top with another tortilla and brush with olive oil.
Cook until golden, about 2 minutes. Turn and cook until other side is golden and cheese is melted, about 2 minutes. Keep warm in oven until ready to serve.
Repeat with remaining ingredients to make 6 quesadillas. Cut into quarters and serve with sour cream, salsa and guacamole.
Makes 12 servings.