Place rack in lowest position in oven. Heat oven to 450 degrees F ( 230 degrees C).
To Make Topping: Mix 1 cup flour, 1/2 cup brown sugar, 1/2 cup white sugar and 1 teaspoon cinnamon; cut in butter or margarine until mixture is moist and crumbly, and clumps together easily.
To Make Filling: Peel, core, and slice apples into approximately 1/8 inch slices. If you cut them too thick you'll have crunchy apples. In another bowl, toss cut up apples, white sugar, lemon juice, 1 teaspoon cinnamon and nutmeg. Sprinkle in flour, and stir until apples are evenly coated.
Layer apple slices in pie shell. You will have a lot of apples, but they will shrink. Layer them higher in the middle. Pour left over juice from apple mixture over apples. Pat the brown sugar topping evenly over apples to make a top crust.
Place pie on cookie sheet in oven to catch juice droppings. Bake for 15 minutes. Reduce oven temperature to 350 degrees F (175 degrees C), and bake for 45 minutes to one hour; bake until center of pie has no resistance. If top starts to get too dark, cover with piece of foil. Cool on wire rack before serving.