Pre-heat the oven to 375° F, and grease an 8x8 or 7x9 baking dish with cooking spray.
Add the sliced apples to a large mixing bowl.
In a small bowl, mix together the sugar, brown sugar, corn starch, cinnamon, and nutmeg.
Add the sugar mixture, sour cream, and lemon juice in with the apples, and mix everything together well.
Pour the apple mixture into a greased baking dish, and thinly slice the butter around on top of the apples.
Bake the apples at 375° F for about 30 to 45 minutes, or until the apples are tender, softened, and bubbly. Be sure to give the apples a good stir halfway thru baking.
Serve the baked apples with a dollop of whipped topping or a generous scoop of vanilla ice cream.