Preheat oven to 350 degrees. Spray 9 x 5 loaf pan with non-stick spray.
Mix together 1/3 cup brown sugar and 1 teaspoon cinnamon in a small bowl. Set aside.
Combine 1 1/2 cups flour and 1 3/4 teaspoons baking powder together in another small bowl and set aside.
In a large bowl, beat 2/3 cup granulated sugar and 1/2 cup softened butter with an electric mixer until smooth and creamy.
Beat in 2 eggs, one at a time until blended. Add 1 1/2 teaspoons vanilla extract, stir until combined.
Add flour mixture to creamed butter mixture and mix until blended.
Mix 1/2 cup milk into batter and continue mixing until smooth.
Pour half the batter into the prepared pan; add half the chopped apple mixture.
Sprinkle 1/2 of the cinnamon-brown sugar mixture on top of apple layer.
Pour the remaining batter over apple layer and top with remaining chopped apples, then the remaining cinnamon-brown sugar mixture.
Lightly pat apples into batter; swirl cinnamon-brown sugar mixture through apples using knife.
Bake in preheated oven until a toothpick inserted in the center of the loaf comes out clean, approximately 60 minutes.
To make glaze, mix together 1/2 cup powdered sugar and 2 to 3 tablespoons milk or cream until well mixed.
Let loaf rest in pan for about 15 minutes before removing from pan. Cool completely on cooling rack. Drizzle with glaze.