Preheat the oven to 350 degrees F (175 degrees C). Coat a 9×5-inch loaf pan with cooking spray.
Combine apples, 2 tablespoons sugar, and 1 teaspoon cinnamon together in a bowl; mix until coated. Mix brown sugar and remaining cinnamon in a second bowl. Whisk flour and baking powder together in a third bowl. Set aside.
Mix remaining white sugar and butter together in a medium bowl with an electric mixer until smooth and creamy. Beat in eggs, 1 at a time, until blended in. Add vanilla extract. Stir in flour mixture until smooth. Add milk and mix until smooth.
Pour about 1/2 of the batter mixture into the prepared loaf pan. Add 1/2 half of the apple mixture, and lightly press the apples into the batter. Sprinkle 1/2 of the brown sugar mixture onto the apples. Pour the remaining batter into the pan, add the remaining apples, and brown sugar mix. Press the apples lightly into the top batter.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour and 15 minutes. Remove from the oven and let cool for 20 minutes.
While loaf cools, pour confectioners’ sugar into a bowl and slowly add in milk. Stir until completely mixed, adding more milk if you want your glaze thinner. Drizzle onto the cooled loaf.