Preheat oven to 350 degrees F. Spray a 9-by-5-inch loaf pan with nonstick spray and line with parchment paper, with ends hanging over edge of pan. Spray parchment with nonstick spray.
Mix brown sugar and 1 teaspoon cinnamon together in a bowl; set aside. Toss apples with 2 tablespoons granulated sugar and remaining teaspoon cinnamon in another bowl; set aside.
Beat butter and remaining 2/3 cup granulated sugar together with mixer until light and fluffy, about 5 minutes. With the mixer on medium speed, add the eggs, 1 at a time; add vanilla extract.
Whisk flour, baking powder and salt together in another bowl, then add to creamed butter mixture and beat until blended. Mix 1/2 cup milk into batter until smooth.
Pour half the batter into the prepared loaf pan; add half the chopped apple mixture.
Sprinkle half of the brown sugar/cinnamon mixture on top of apple layer.
Pour the remaining batter over apple layer and top with remaining chopped apples, then the remaining brown sugar/cinnamon mixture.
Lightly pat apples into batter; swirl brown sugar mixture through apples using a knife.
Bake until a toothpick inserted in the center of the loaf comes out clean, approximately 1 hour and 10 minutes. Watch bread and cover with foil during last 10 minutes of baking time to prevent overbrowning if needed.
Let loaf rest in pan for 15 minutes , then remove from pan using edge of parchment and place on wire rack to cool completely.