Place a large skillet on grill side burner. In the skillet, cook apples and ginger in butter over medium heat about 3 minutes or until apples are just tender. Stir in brown sugar. In a small bowl, combine apple juice and cornstarch; add to skillet. Cook and stir until thickened and bubbly. Cook and stir for 2 minutes more. Cool slightly.
Scoop ice cream into dessert dishes. Spoon apple mixture over ice cream. Makes 4 servings.