In a 2 quart baking dish or an 8x8 pan, add the butter and brown sugar. Place the pan in the oven to melt the butter for about 1-2 minutes. Keeping an eye on it so it doesn't burn. As soon as it starts melting, remove from the oven and stir the butter and brown sugar together. Set aside.
Using a mixer, beat the egg whites until stiff peaks form. Set aside.
In a different bowl, add the egg yolks and white sugar, beating well. Stir in the vanilla extract.
In a small bowl, combine flour, salt and baking powder. Add the flour mixture alternately with the water to the egg yolk mixture. Stir until just combined.
Peel and core your apples, then cut into large chunks. Arrange apple pieces over the brown sugar mixture in the pan.
Pour batter over apples.
Bake for about 45 minutes until the top is golden brown. Enjoy with vanilla ice cream or whipped topping!