Susan serves these with homemade pico de gallo, but purchased salsa also works well.
8 appetizer or 4 Main-course servings
Place steak in glass dish. Sprinkle steak on both sides with lime juice, salt and pepper. Let stand at least 15 minutes and up to 1 hour, turning steak occasionally.
Preheat oven to 375°F. Heat 1 tablespoon oil in heavy large skillet over high heat. Add steak and sauté to desired doneness, about 3 minutes per side for rare. Transfer steak to cutting board. Let rest 5 minutes; slice thinly.
Brush 4 tortillas with oil; place tortillas, oil side down, on 2 baking sheets. Spread 1/4 cup cheese and 1 tablespoon pico de gallo on each tortilla. Top each with second tortilla. Spread each with 1/4 cup cheese, 1/4 of steak and 1 tablespoon pico de gallo. Press third tortilla onto each stack. Brush top tortillas with oil.
Bake quesadillas 10 minutes. Using metal spatula, turn each over. Continue to bake until heated through and golden, about 10 minutes longer. Transfer quesadillas to plates. Cut into wedges. Serve with remaining pico de gallo.