Preheat Oven:

Preheat your oven to 350°F (175°C). Grease a 9x9-inch baking dish or loaf pan and set aside.

Prepare the Apple Filling:

In a medium bowl, toss the diced apples with granulated sugar, cinnamon, and nutmeg until evenly coated. Set aside.

Make the Cake Batter:

In a large bowl, cream the softened butter with the granulated sugar and brown sugar using an electric mixer until light and fluffy. Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, alternating with the milk, beginning and ending with the dry ingredients. Mix just until combined.

Layer the Cake:

Pour half of the cake batter into the prepared baking dish, spreading it evenly. Add half of the apple mixture on top of the batter. Pour the remaining batter over the apples, spreading it carefully. Top with the remaining apples, pressing them slightly into the batter.

Bake:

Bake in the preheated oven for 45–55 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool for 10–15 minutes.

Make the Glaze:

While the cake cools, whisk together the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Adjust the consistency with more milk if needed.

Glaze the Cake:

Drizzle the glaze generously over the warm cake, allowing it to seep into the top. Let the cake cool completely before slicing and serving.