Preheat your oven to 350°F (175°C) and grease a 9×5-inch loaf pan.
In a small bowl, mix together the chopped apples, 1/4 cup granulated sugar, and 1 teaspoon ground cinnamon. Set aside.
In a large bowl, whisk together the flour, 1/2 cup granulated sugar, light brown sugar, salt, baking powder, and 1/2 teaspoon cinnamon.
In another bowl, beat the eggs, melted butter, milk, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix.
Pour half of the batter into the prepared loaf pan. Add half of the apple mixture on top of the batter. Pour the remaining batter over the apples and top with the remaining apple mixture. Lightly press the apples into the batter.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
While the bread is baking, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract until smooth.
Once the bread is done, allow it to cool in the pan for about 10 minutes before transferring it to a wire rack. Drizzle the glaze over the warm bread.