Preheat the Oven
Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round or square cake pan, or line it with parchment paper.
Mix the Dry Ingredients
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Combine the Wet Ingredients
In a large mixing bowl, beat the eggs, granulated sugar, and brown sugar until light and fluffy. Add the vegetable oil, vanilla extract, and milk, mixing until well combined.
Incorporate the Dry Ingredients
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Avoid overmixing, as this can make the cake dense.
Fold in the Apples
Gently fold the chopped apples and nuts (if using) into the batter, ensuring they are evenly distributed.
Bake the Cake
Pour the batter into the prepared pan and spread it evenly. Bake for 35-40 minutes, or until a toothpick inserted in the center comes out clean.