Preheat oven to 350 degrees. Grease and line a 9x5 inch bread pan with parchment paper. In a small bowl, mix the white sugar and cinnamon and set aside.
In a stand mixer or large bowl, combine brown sugar and butter until smooth. Add eggs and vanilla and beat on medium speed until combined. Add flour, baking powder, cinnamon, salt, and finally the milk.
Pour half of the batter into the pan. Top that with half of the chopped apples. Pat the apples into the batter and then sprinkle half of sugar and cinnamon mixture. Pour the rest of the batter over the cinnamon sugar mixture, then top with remaining apples and add what is left of the cinnamon sugar mixture. Press the topping into the batter.
Bake for 45-50 minutes or until a toothpick inserted in the middle of the loaf comes out clean (be careful not to overcook or it will become tough).
Let it stand in the pan for 10-15 minutes, then using the sides of the parchment paper that stick out, lift and place on a cooling rack to finish cooling.