Preheat your oven to 350°F (175°C). Grease the loaf pan with butter or non-stick spray.
In a mixing bowl, whisk together the flour, granulated sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, combine the milk, melted butter, eggs, and vanilla extract. Mix until well combined.
Pour the wet ingredients into the dry ingredients and stir gently until just combined.
Fold in the diced apples, ensuring they are evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan, smoothing the top with a spatula.
Bake in the preheated oven for 50 minutes, or until a toothpick inserted in the center comes out clean.
While the bread is baking, prepare the glaze by whisking together the powdered sugar and milk in a small bowl until smooth.
Once the bread is done baking, remove it from the oven and let it cool in the pan for 10 minutes before transferring it to a wire rack.
Drizzle the glaze over the warm bread and allow to set for a few minutes before slicing.