Preheat your oven to 350°F (175°C). Spray a 9x5-inch loaf pan with non-stick cooking spray. For easy removal, you can also line the pan with foil or parchment paper and spray that with non-stick spray as well.
In a small bowl, combine 1/3 cup light brown sugar and 1 teaspoon ground cinnamon; set aside for later layering. In a separate bowl, whisk together 1 1/2 cups all-purpose flour and 1 3/4 teaspoons baking powder. Set this mixture aside as well.
In a large mixing bowl, beat together 2/3 cup granulated sugar and 1/2 cup softened unsalted butter until creamy and light. Add the eggs one at a time, beating well after each addition. Stir in 1 1/2 teaspoons vanilla extract. Gradually add the flour mixture from Step 2, alternating with 1/2 cup milk (or almond milk), mixing until a smooth batter forms.
Peel and dice the 2 large apples into small pieces. Toss them in a bowl with 2 tablespoons granulated sugar and 1 teaspoon ground cinnamon until they are fully coated.
Pour half of the batter from Step 3 into the prepared loaf pan and spread it out evenly. Top with half of the cinnamon apple mixture from Step 4, then sprinkle half of the brown sugar-cinnamon mixture from Step 2 over the apples. Repeat with the remaining batter, apples, and brown sugar-cinnamon mixture to create a second layer. Use a knife to gently swirl through the layers a few times, creating a marbled effect. I like to swirl deeply to get ribbons of cinnamon sugar throughout every slice.
Bake the assembled loaf in the preheated oven for about 60 minutes, or until a toothpick inserted into the center comes out clean. Let the bread rest in the pan for about 15 minutes, then remove it from the pan and transfer to a cooling rack to cool completely before glazing. For best texture, avoid slicing while it's still hot.
In a small bowl, mix 1/2 cup powdered sugar with 1 to 3 tablespoons milk or cream until smooth and pourable. If the glaze is too thick, microwave it for 10 seconds to help it drizzle easily. Once the apple bread has fully cooled, drizzle the glaze over the top. If you prefer a thicker layer of glaze, I like to double the recipe—you can never have too much glaze on apple bread!