Preheat your oven to 350°F (175°C) and prepare the Bundt pan.
In a mixing bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt; set aside.
In another bowl, cream the softened butter, granulated sugar, and brown sugar together until light and fluffy.
Add in the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
Gradually add the dry mixture to the wet ingredients, alternating with the chopped apples, and fold gently until combined.
If using, fold in the chopped walnuts or pecans for added texture.
Pour the batter into the prepared Bundt pan, smoothing the top with a spatula.
Bake for 55-65 minutes, or until a toothpick inserted in the center comes out clean.
Once baked, allow the cake to cool in the pan for 10-15 minutes, then invert onto a wire rack to cool completely.
Whisk together powdered sugar and milk to create a glaze, adjusting the consistency as needed.
Drizzle the glaze over the cooled Bundt cake, allowing it to set before serving.