Combine flour, sugars, and cinnamon in large bowl (or food processor bowl.)
Cut in butter cubes until mixture forms large clumps. (In food processor pulse 8 to 10 times.)
Stir in oatmeal and set aside.
Preheat oven to 375°F. In a small bowl combine sugar, cinnamon, red pepper and cornstarch; set aside.
Combine apple slices and chopped ginger root. Stir in sugar/cornstarch mixture. Spread apple mixture in a 9-inch square baking pan.
Sprinkle topping evenly over the apples. Bake for 45 minutes or until apples are bubbly and the topping is golden brown.