1. Heat the oven to 350°F (175°C) with a rack in the center. Grease a 9×5-inch loaf pan, line it with a parchment sling overhanging the long sides, and lightly grease the parchment.

2. Stir the brown sugar and 1 1/2 teaspoons cinnamon together in a small bowl. Peel, core, and dice the apples into 1/2-inch pieces; toss them with 2 tablespoons granulated sugar and 1 teaspoon cinnamon. Set both aside.

3. Whisk the flour, baking powder, and salt in a bowl. In a large bowl, beat the butter and 2/3 cup granulated sugar on medium speed about 2 minutes, until pale and fluffy. Beat in the eggs one at a time, then the vanilla and sour cream, scraping the bowl.

4. On low speed or by hand, add half the flour mixture, then the milk, then the remaining flour, mixing only until no dry streaks remain. The batter should be thick.

5. Spread half the batter in the pan. Top with half the apples (leave any juices in the bowl) and half the brown sugar mixture. Swirl gently with a butter knife in a few figure-eights.

6. Spread the remaining batter over the top, add the remaining apples, press them lightly into the surface, and sprinkle with the remaining brown sugar mixture. Swirl once more, keeping the knife shallow.

7. Bake 55 to 65 minutes, tenting loosely with foil after about 40 minutes if the top browns quickly. The loaf is done when a toothpick in the center comes out with only a few moist crumbs and the center of the cake (not an apple) reads 200–205°F (93–96°C).

8. Cool in the pan on a rack for 15 minutes. Loosen the short ends, lift the loaf out with the parchment, and cool completely on the rack, about 1 1/2 hours.

9. Whisk the powdered sugar, 1 1/2 tablespoons milk, vanilla, and salt until smooth, adding the remaining milk a few drops at a time only if needed for a slow ribbon. Drizzle over the cooled loaf and let set about 20 minutes. Slice with a serrated knife into 10 slices.