Preheat your oven to 350°F (175°C). Grease a 9×5-inch loaf pan with butter or non-stick spray, or line it with parchment paper for easy removal.
In a small bowl, toss the chopped apples with the brown sugar and cinnamon until they are evenly coated. Set this mixture aside so the apples can start to release their juices.
In a large mixing bowl, beat the softened butter and granulated sugar together until the mixture is light and fluffy. This should take about 2-3 minutes using a hand mixer or stand mixer.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract until fully incorporated.
Whisk together the flour and baking powder in a separate bowl. Gradually add the dry ingredients to the butter mixture, alternating with the milk. Start and end with the flour mixture, mixing just until combined. Do not overmix.
Pour half of the batter into the prepared loaf pan. Top with half of the apple mixture. Pour the remaining batter over the apples, and then top with the rest of the apple mixture. Use a knife to gently swirl the apples into the batter.
Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean. If the top starts to brown too quickly, you can cover it loosely with foil for the last 15 minutes.
Whisk the powdered sugar and 1 tablespoon of milk together to create a thick glaze. While the bread is still slightly warm, drizzle the glaze over the top. Let the bread cool completely before slicing.