Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan to prevent sticking. Make sure to coat the pan well so your bread comes out easily after baking.
In a small bowl, combine 1/3 cup brown sugar and 1 teaspoon ground cinnamon to make the cinnamon sugar for layering. Set this mixture aside. In another bowl, toss the peeled and chopped apples with 2 tablespoons sugar and 1 teaspoon ground cinnamon. Set the apple mixture aside as well. Having these prepared will make assembling the bread much easier later.
With an electric mixer, cream together 1/2 cup softened butter and 2/3 cup sugar until the mixture is light and fluffy. Beat in the eggs one at a time, then add 1 1/2 teaspoons vanilla extract. In a separate bowl, stir together 1 1/2 cups flour and 1 3/4 teaspoons baking powder. Gradually add the dry ingredients into the creamed mixture. Finally, mix in 1/2 cup milk until everything is well combined. The batter will be fairly thick, which helps support the apple filling.
Pour half of the prepared batter into your greased loaf pan and spread it evenly. Layer half of the apple mixture (from Step 2) on top of the batter. Sprinkle half of the reserved cinnamon sugar mixture (from Step 2) over the apples. Repeat the layering with the rest of the batter, apples, and cinnamon sugar. This helps ensure each slice has a delicious swirl of apple and cinnamon. I like to give the top a gentle swirl with a knife for a prettier finish, though that’s optional.
Bake the assembled loaf in the preheated oven for 55–60 minutes, or until a toothpick inserted into the center comes out clean. If the loaf starts browning too quickly, loosely cover it with foil halfway through baking. Allow the bread to cool in the pan for about 20 minutes before removing it to slice. Letting it rest first really helps keep the bread moist when you slice it.
Whisk together 1/2 cup powdered sugar and 3 tablespoons milk in a small bowl until smooth. Drizzle the icing over the slightly cooled bread. Slice and serve—enjoy! I find that the drizzle not only looks beautiful but adds a lovely sweetness to each bite.