Pre-heat the oven to 425° F.
Core, peel, and slice the washed apples, and add them to a greased 9x13 baking dish.
In a large mixing bowl, stir together the flour, baking powder, salt, cinnamon, sugar, and brown sugar.
Using a pastry blender, mix the dry ingredients with the unbeaten eggs and melted butter, forming a kind of crumble topping.
Crumble the topping right over the apples.
Bake, uncovered, at 425° F for about 20 minutes; the crust should be a nice golden brown. Then cover with aluminum foil, and bake an additional 10 to 15 minutes, 'til the apples are tender.
Once you've removed it from the oven, allow it to cool for about 15 minutes before serving.
Serve with a scoop of vanilla ice cream or a swirl of whipped cream.