Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan and line it with parchment paper, leaving a little overhang on the sides.
Whisk the flour, baking powder, and salt together in a medium bowl. Set aside.
Place the chopped apples in another bowl. Add the brown sugar and cinnamon and toss until all the pieces are coated. Let the apples sit while you prepare the batter.
Add the softened butter and granulated sugar to a large mixing bowl. Beat for 2 to 3 minutes, until noticeably lighter and creamy.
Beat in the eggs one at a time.
Add 2 teaspoons of vanilla and mix until combined.
Add about half of the flour mixture and mix gently.
Pour in the milk and mix briefly.
Add the remaining flour mixture and stir just until no obvious dry streaks remain. Don't overmix. The batter should be thick.
Spoon half of the batter into the prepared loaf pan and spread it toward the edges.
Spoon half of the cinnamon apples over the batter.
Dollop the remaining batter over the apples and carefully spread it out. It doesn't need to be perfectly even.
Add the remaining cinnamon apples over the top, including the cinnamon-brown sugar liquid left in the bowl.
Press the apples very lightly into the batter.
Run a butter knife through the batter two or three times to create loose swirls. Don't completely mix the layers together.
Bake for 55 to 65 minutes, checking the loaf beginning around 50 to 55 minutes.
The bread is ready when the top is golden and a toothpick inserted into several spots near the center comes out without raw batter. A few moist crumbs are fine.
If the top becomes too dark before the center is ready, loosely cover it with foil and continue baking.
Let the loaf cool in the pan for 15 minutes.
Lift it from the pan using the parchment and transfer it to a wire rack. Cool for at least another 20 to 30 minutes.
Add the powdered sugar, 1 1/2 tablespoons milk, and 1/2 teaspoon vanilla to a small bowl.
Whisk until smooth. If necessary, add additional milk one teaspoon at a time until the glaze is thick but drizzleable.
Drizzle the glaze generously over the warm or completely cooled loaf.
Let the glaze set for a few minutes before slicing.