Preheat oven to 350°F (175°C). Butter a 9x5-inch metal loaf pan and line with parchment paper, leaving an overhang on the long sides for easy lifting.

In a small bowl, whisk together the brown sugar and 1.5 teaspoons of cinnamon. In a separate bowl, toss the finely diced apples with 1 tablespoon of flour and 1 tablespoon of the cinnamon-sugar mixture (this prevents apples from sinking).

In a medium bowl, whisk together the flour, baking powder, sea salt, and nutmeg. In a large bowl, whisk the melted butter, granulated sugar, eggs, and vanilla extract until pale and slightly frothy (about 1 minute).

Stir in half the dry flour mixture, followed by the milk, then remaining flour mixture, stirring just until no dry flour streaks remain. Gently fold in 3/4 of the diced apples. Spread half the batter into the prepared loaf pan. Sprinkle 2/3 of the cinnamon-sugar mixture evenly over the batter. Top with remaining batter, smooth gently, then scatter the remaining apples and remaining cinnamon sugar across the surface. Use a butter knife to gently swirl the top layer once or twice.

Bake at 350°F for 50 to 55 minutes, or until the top is golden-brown with a classic center crack and a wooden skewer inserted into the center comes out clean with a few moist crumbs attached (internal temperature reaching 200°F). If top browns too fast at minute 40, tent loosely with aluminum foil.

Let the loaf cool in the pan on a wire rack for 15 minutes. Use parchment handles to lift the loaf onto the rack to cool completely. In a small bowl, whisk powdered sugar, milk, and vanilla into a thick glaze. Drizzle over the cooled loaf. Slice with a sharp serrated knife and serve.