1. Preheat your oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.
2. In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
3. In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, about 3-4 minutes.
4. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
5. Gradually mix in the dry ingredients, alternating with the sour cream, until just combined.
6. Fold in the diced apples and walnuts (if using) gently with a spatula.
7. Pour the batter into the prepared pan and smooth the top with a spatula.
8. Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
9. While the cake is cooling, prepare the frosting. In a medium bowl, beat the cream cheese and butter together until smooth.
10. Gradually add the powdered sugar, beating until fully incorporated and smooth. Stir in the vanilla extract.
11. Once the cake is completely cool, spread the frosting evenly over the top. Slice and serve.

Pro tip from my kitchen: ensure your butter and cream cheese are at room temperature before starting the frosting to achieve a silky smooth texture.