Preheat the oven to 350°F (175°C) and grease a 9-inch cake pan.
Mix brown sugar and cinnamon in a small bowl and set aside.
Cream butter and white sugar in a large bowl until light and fluffy, then add eggs and vanilla extract.
Combine dry ingredients (flour, baking powder) and gradually mix them into the batter, alternating with milk.
Fold in chopped apples gently, ensuring even distribution.
Pour half the batter into the pan, sprinkle with cinnamon-sugar mix, then add the remaining batter and top with more cinnamon-sugar.
Bake for 35 minutes or until a toothpick inserted in the center comes out clean.
Cool for 10 minutes, then slice and enjoy warm!