Preheat the oven to 350°F (175°C). Grease or line a 9x5-inch loaf pan with parchment paper.
Prepare the apples: Toss the chopped apples with 1/4 cup granulated sugar and 1 teaspoon cinnamon. Set aside.
Mix dry ingredients: In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon (if using).
Cream butter and sugar: In a large bowl, beat butter and sugar together until light and fluffy.
Add eggs and vanilla: Beat in eggs one at a time, followed by the vanilla extract.
Combine wet and dry ingredients: Gradually add the dry ingredients to the wet ingredients, alternating with milk. Mix until just combined.
Fold in apples: Gently fold the apple mixture into the batter.
Layer the cinnamon-sugar: Spoon half the batter into the pan, sprinkle with half of the cinnamon-sugar, then add the remaining batter and top with the rest of the cinnamon-sugar.
Bake for 60-70 minutes, or until a toothpick inserted in the center comes out clean.
Cool for 10 minutes in the pan, then transfer to a wire rack to cool completely.
Make the glaze: Whisk together powdered sugar, milk, and vanilla extract until smooth. Drizzle over the cooled bread.