In a bowl, combine the flour, baking powder, and salt.
Put the first stick and a half of butter in a mixing bowl, along with sugar and vanilla. Beat those together until smooth.
Mix in half of your flour mixture, then your milk, and then the rest of the flour mixture. Combining each addition completely before the next. Set it aside.
In a bowl, beat the egg whites until they are stiff.
Carefully fold these into the thick batter, until just combined.
Spread the batter into the cake pan.
Core and slice up the apple. I leave the skin on, but that is up to you.
Arrange the slices over the top of the cake batter.
In another bowl, stir together the 3/4 cup of flour, brown sugar, cinnamon, and the chopped pecans. Add in the remaining butter. Mix until this is completely combined and crumbly. I find that this mixes best with a whisk or a fork.
Sprinkle the mixture all over the top of the apples. Bake this cake for about 40 - 50 minutes until the cake is firm in the middle, or tests done when stuck with a toothpick.