Preheat oven to 375 degrees F (190 degrees C). Grease an 8x8 inch baking dish.
In a large bowl, combine the apples, 1/2 cup brown sugar, cinnamon and nutmeg. Place in prepared baking dish.
In a medium bowl, combine the flour, oats and 3/4 cup brown sugar. Cut in butter until mixture resembles coarse crumbs. Sprinkle over the apple mixture.
Bake for 35 to 40 minutes in preheated oven until topping is golden brown.