Preheat Oven: Preheat your oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan.
Prepare Dry Ingredients: In a medium bowl, whisk together flour, baking powder, salt, cinnamon, and nutmeg. Set aside.
Mix Wet Ingredients: In a large bowl, beat eggs, granulated sugar, and brown sugar until smooth. Add melted butter, vanilla, and milk. Mix well.
Combine Wet and Dry Ingredients: Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Prepare the Cinnamon Sugar Swirl: In a small bowl, mix granulated sugar and cinnamon for the swirl.
Layer the Bread: Pour half of the batter into the loaf pan. Sprinkle half of the cinnamon sugar mixture over the batter. Add the chopped apples, then top with the remaining batter and sprinkle the remaining cinnamon sugar over the top.
Swirl the Sugar: Use a knife or toothpick to gently swirl the cinnamon sugar through the batter.
Bake: Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. If the top is browning too quickly, cover with foil and continue baking.
Make the Glaze: While the bread cools, whisk together powdered sugar, milk, and vanilla for the glaze.
Cool and Glaze: Let the bread cool in the pan for 10 minutes before transferring it to a wire rack. Drizzle with the glaze once cooled.