Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper for easy removal.
In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, salt, 1 teaspoon of cinnamon, and nutmeg.
In a separate bowl, combine the melted butter, milk, eggs, and vanilla extract. Mix well until fully combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Gently fold in the diced apples until evenly distributed throughout the batter.
In a small bowl, mix together the brown sugar and 1 teaspoon of cinnamon for the topping.
Pour half of the batter into the prepared loaf pan. Sprinkle half of the brown sugar mixture over the batter. Add the remaining batter on top and finish with the rest of the brown sugar mixture.
Use a knife or skewer to swirl the topping into the batter for a marbled effect.
Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.
For the glaze, whisk together the powdered sugar and 2 tablespoons of milk until smooth. Drizzle over the cooled bread before slicing.