Preheat your oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan.
In a small bowl, mix together the brown sugar and cinnamon. Set aside.
In a large mixing bowl, cream together the white sugar and softened butter until smooth. Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
Combine the flour and baking powder. Gradually add this mixture to the creamed mixture, alternating with the milk. Mix until just combined.
Pour half of the batter into the prepared loaf pan. Top with half of the chopped apples and half of the brown sugar-cinnamon mixture. Lightly press the apples into the batter.
Pour the remaining batter over the apple layer. Top with the remaining chopped apples and brown sugar-cinnamon mixture, again pressing lightly into the batter.
Bake in the preheated oven for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for about 15 minutes, then remove from the pan and transfer to a wire rack to cool completely.
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