Preheat your oven to 350°F and line a 1-pound loaf pan with parchment paper on all sides.

In a small bowl, mix the chopped apples with 2 tablespoons of dark brown sugar and 1 teaspoon of ground cinnamon. Toss to combine and set aside.

In another small bowl, combine ⅓ cup of brown sugar with 2 teaspoons of cinnamon and stir to mix. Set this aside as well.

In a stand mixer with a paddle attachment, cream together the butter and granulated sugar on medium speed until the mixture is light and fluffy. Use a silicone spatula to scrape down the sides of the bowl.

Add the eggs one at a time, beating at low speed and scraping down the bowl after each addition. Then, mix in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and salt.

With the mixer on low speed, add half of the dry ingredients and mix just until combined. Then, add the milk and sour cream, mixing slightly.

Finally, add the remaining dry ingredients and mix until just combined, ensuring there are no streaks of flour.

Transfer half of the batter into the prepared loaf pan and spread it into an even layer. Top this layer with half of the cinnamon apples and sprinkle with half of the cinnamon sugar mixture.

Spoon the remaining batter over the apples, spreading it evenly. Then, add the rest of the apples and sprinkle the remaining cinnamon sugar on top.

Bake the loaf for 50 to 55 minutes, or until it is golden brown and a butter knife inserted into the center comes out clean.

Allow the loaf to cool. While it cools, prepare the glaze by whisking together the powdered sugar, 1 tablespoon of milk, and ¼ teaspoon of vanilla extract until smooth.

Once the loaf has cooled, drizzle the glaze over the top and serve.