Preheat oven to 350°F and grease a 9×5-inch loaf pan.
Whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg in a large bowl.
In another bowl, beat eggs, granulated sugar, brown sugar, melted butter, milk, and vanilla until combined.
Fold dry ingredients into wet mixture just until blended.
Stir in diced apples evenly throughout the batter.
Pour batter into prepared loaf pan and smooth the top.
Bake for 50–60 minutes or until a toothpick inserted in the center comes out clean.
Cool in pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.
