Preheat your oven to 350°F (175°C). Grease a 9x5 inch loaf pan or line it with parchment paper.

Combine 1/3 cup light brown sugar and 1 teaspoon ground cinnamon in a small bowl. Toss the diced apples in the mixture and set aside.

In a large mixing bowl, cream together 2/3 cup white sugar and 1/2 cup softened unsalted butter until light and fluffy.

Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Mix in 1 1/2 teaspoons of vanilla extract.

Sift together 1 1/2 cups all-purpose flour and 1 3/4 teaspoons baking powder. Gradually add the dry ingredients to the wet mixture, alternating with 1/2 cup milk. Mix just until combined.

Pour half of the batter into the loaf pan and smooth the top. Add half of the cinnamon-sugar-coated apples and press gently. Repeat with the remaining batter and apples, swirling with a knife for a marbled effect.

Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Allow the bread to cool for 10 minutes in the pan, then transfer to a wire rack to cool completely.

Mix 1/2 cup powdered sugar with 2-3 tablespoons of milk or cream until smooth. Drizzle over the cooled bread.