Heat coals or gas grill for direct heat. Place 2 of the tortillas on cookie sheet. Sprinkle each with 1/2 cup of the cheese. Top each with half of the pepperoni. Sprinkle 1/2 cup of remaining cheese over each. Top each with tortilla.
Transfer quesadillas to grill 4 to 6 inches from low heat. Cover and grill 2 to 3 minutes, rotating occasionally, until bottom tortilla is golden brown. Turn over with broad pancake turner. Cover and grill 2 to 3 minutes longer or until bottom tortilla is golden brown.
Transfer quesadillas back to cookie sheet. Cut each quesadilla into 8 wedges. Serve with pizza sauce.