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Preheat your oven to 350°F (175°C). Grease a 9×5 inch loaf pan with non-stick cooking spray or line it with foil and spray with non-stick cooking spray to ensure easy removal.
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In one bowl, combine 1/3 cup of light brown sugar and 1 teaspoon of cinnamon. In another bowl, mix 2 chopped apples with 2 tablespoons of granulated sugar and the remaining teaspoon of cinnamon.
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In a medium bowl, beat 1/2 cup of softened butter and the remaining 2/3 cup of granulated sugar together with an electric mixer until the mixture is smooth and creamy, which takes about 5 minutes. Add the eggs one at a time and blend in, followed by 1 1/2 teaspoons of vanilla extract.
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In another bowl, whisk 1 1/2 cups of all-purpose flour and 1 3/4 teaspoons of baking powder together. Add this mixture to the creamed butter mixture and beat until well blended. Stir in 1/2 cup of milk or almond milk until the batter is smooth.
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Pour half of the batter into the prepared loaf pan, followed by half of the apple mixture. Sprinkle half of the brown sugar and cinnamon mixture on top of the apples. Repeat with the remaining batter, apples, and brown sugar and cinnamon mixture. Swirl the brown sugar mixture through the apples using a knife or spoon.
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Bake the loaf in the oven until a toothpick inserted in the center comes out clean, which takes approximately 1 hour and 10 minutes.
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For the glaze, mix 1/2 cup of powdered sugar with 1 to 3 tablespoons of milk depending on the desired thickness. Let the loaf cool for about 15 minutes, then drizzle the glaze over it.
