In a separate bowl, mix 1/2 cup flour, 1/2 stick butter, & 3/4 cup brown sugar until crumbly. Stir in 3/4 cup cheddar cheese (if you don't want it chewy but still want to add the cheddar taste, use a handful of crushed cheddar crackers, like cheese its).
Pour this crumb mixture over the apple pie filling. Bake at 350 for 15-20 minutes. Serve warm.