Begin by preheating your oven to 350 degrees F.
Line an 8 x 4 loaf pan with parchment paper and spray with baking spray. Set aside.
In a medium bowl, toss together the chopped apples, brown sugar, and cinnamon. Set aside.
In another medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, beat together the granulated sugar and butter until combined. Then, beat in the eggs one at a time. Next, beat in the milk and vanilla extract.
Add the flour mixture and stir with a spatula until just combined.
Add half of the batter to your prepared loaf pan, then top with half of the apple mixture.
Spread the remaining batter over the top, then top with the remaining apple mixture.
Gently pat the apples into the batter. Then, use a butter knife to swirl the apples into the batter. (Two to three swirls are all you need.)
Bake for 55-60 minutes or until a toothpick inserted in the center comes out clean. (Cover the loaf with foil for the last 15-20 minutes of baking to prevent over-browning.)
Cool in the pan on a wire rack for about 10 minutes. Then, use the parchment paper to lift the loaf from the pan. Cool completely on a wire rack.
In the meantime, prepare the icing by whisking together the sour cream, vanilla extract, and powdered sugar. Add in the milk, 1 teaspoon at a time, to achieve a drizzling consistency.
Drizzle your loaf with the icing before slicing and serving.