Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line it with parchment paper.
Peel and finely dice the apples. Toss them with brown sugar, cinnamon, nutmeg, and flour. Set aside.
In a medium bowl, whisk together flour, baking powder, salt, cinnamon, and nutmeg.
In a large bowl, beat softened butter and granulated sugar until light and creamy.
Add the eggs one at a time, mixing well after each addition. Stir in vanilla extract.
Gradually add the dry ingredients, alternating with the milk. Mix just until combined.
Spread half of the batter into the prepared loaf pan.
Add half of the seasoned apples and sprinkle with some of the cinnamon-brown sugar mixture.
Spread the remaining batter over the apple layer.
Add the remaining apples and cinnamon mixture to the top.
Drizzle the melted butter evenly over the topping.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
If the top browns too quickly, loosely cover with foil during the final 15 minutes.
Cool in the pan for about 15 minutes, then transfer to a wire rack.
Whisk powdered sugar, milk, and vanilla until smooth.
Drizzle the glaze over the cooled bread before slicing and serving.