Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan.

In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

In a large bowl, cream together the butter and granulated sugar until light and fluffy.

Add the eggs one at a time to the butter mixture, beating well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredients to the wet mixture, alternating with milk. Start and finish with the dry ingredients, mixing just until combined.

Gently fold in the diced apples until evenly distributed throughout the batter.

Pour the batter into the prepared loaf pan, smoothing the top with a spatula.

In a small bowl, mix the brown sugar and ground cinnamon for the topping. Sprinkle evenly over the batter.

Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean.

Remove the bread from the oven and let it cool in the pan for 10 minutes before transferring to a wire rack to cool completely.