Spread sauce on one side of each tortilla, leaving a 1/2" border. Sprinkle about 1/4 cup cheese atop pizza sauce on half of each tortilla; top with pepperoni and a light sprinkle of additional cheese. Fold tortillas in half; press gently. Using pastry brush, very lightly brush both sides of each tortilla with a bit of oil. Heat nonstick griddle over medium heat; cook tortillas, 2 or 3 at a time, until cheese melts and tortilla turns golden and lightly crispy, turning once (about 4 min. total).
To Serve: Let rest 1 min. before cutting each quesadilla in half.