Preheat oven to 350°F. Spray an 8.5 x 4.5 x 2.5-inch loaf pan with cooking spray.
In a small bowl, whisk together 1/3 cup brown sugar and 1 teaspoon cinnamon. Set aside.
In a large mixing bowl, cream together the softened butter and 2/3 cup granulated sugar on medium speed for 3-4 minutes until pale and fluffy.
Add eggs one at a time, beating well after each addition. Add vanilla extract and mix until combined.
In a separate bowl, whisk together flour and baking powder.
Add the flour mixture to the butter mixture gradually, stirring gently until just combined. Add 1/2 cup milk and mix until smooth. Do not overmix.
In a small bowl, toss the chopped apples with 1 tablespoon sugar and 1 teaspoon cinnamon. Coat well.
Pour half of the batter into the prepared loaf pan and spread evenly. Spoon half of the apple mixture over the batter.
Carefully spread the remaining batter over the apples. Top with the remaining apple mixture, pressing down slightly.
Sprinkle the brown sugar and cinnamon topping generously over the entire surface.
Bake for 60 minutes, or until a toothpick inserted in the center comes out clean or with just a few moist crumbs. If the top browns too quickly after 40 minutes, loosely tent with aluminum foil.
Let the bread cool in the pan for 30 minutes before removing.
While the bread cools, whisk together powdered sugar and 1 tablespoon milk in a small bowl until smooth. Adjust consistency by adding more sugar (if too thin) or milk (if too thick).
Drizzle the glaze over the cooled bread in a zigzag pattern. Let the glaze set before slicing.