Preheat your oven to 400�F.
In a large bowl, mix eggs and sugar until light and fluffy using a handheld mixer.
Add melted butter, milk, and vanilla to the mixture, and beat until well combined.
Sift flour, salt, and baking powder into the bowl, then beat again until smooth.
Quarter, core, and peel the apples, then slice them thinly (about 1 to 2 mm thick). Add slices to the bowl as you go.
Toss the sliced apples with the batter until they're all coated.
Butter and flour an 8" x 8" baking dish. Pour in the apple-batter mix, shaking lightly to remove air pockets and smoothing out the top.
Bake for 35 minutes. Let it cool in the dish before serving, and don't forget to sprinkle with cinnamon for that extra flavor!