Melt 1 tablespoon butter in a large nonstick skillet over medium-high heat; add apple mixture, and sauté 5 to 8 minutes or until apples are tender. Remove apple mixture from skillet; wipe skillet clean.
Stir together cream cheese and powdered sugar until smooth. Spread cream cheese mixture evenly on 1 side of each tortilla; top cream cheese mixture evenly with apple mixture. Fold tortillas in half over apple mixture.
Melt 1 tablespoon butter in skillet over medium heat. Cook 2 quesadillas 2 minutes on each side or until golden brown. Repeat procedure with remaining butter and quesadillas. Drizzle with caramel sauce, and top with vanilla ice cream. Serve immediately.