Melt 2 tablespoons butter in a frying pan.
Dice apples (peel if you choose). Put apples, cinnamon and brown sugar in frying pan and cook until apples are soft and syrup has formed. Set aside and allow it to cool.
Sift flour, baking powder and salt; set aside.
Melt the remaining butter, cool and beat it with the egg and sugar. Add milk and vanilla. Mix liquid batter into the flour mixture. Fold in apples, reserving the syrup for topping. Pour batter into a greased and floured 8x8" cake pan.
For the topping, mix together the sugar, flour and syrup from the apples. Add more brown sugar or flour as needed. Sprinkle over the top of the batter, covering completely.
Cover with foil and bake at 375° for 10 minutes. Remove the foil and cook for another 10-15 minutes or until a tooth pick inserted comes out clean.