Preheat oven to 350 degrees
Butter and flour a 8 X 8 inch glass dish, tapping the flour to remove the excess
Mix the eggs and sugar in a mixing bowl, on a medium setting, for 5 minutes
Gradually add the flour, milk and butter, scraping down the sides of the bowl after each addition. When each ingredient is added, mix on medium setting for 5 minutes
Add the baking powder and vanilla; mix an additional 2 minutes on medium setting
Pour batter into dish, and arrange the apple slices in whatever pattern you'd like, on top
Bake for 50 minutes, or until a wooden toothpick inserted in the middle of the cake comes out clean
Remove from oven and let cool 10 minutes
Serve immediately or refrigerate overnight (pairs nicely with vanilla ice cream)