Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg. Set aside.
In a large bowl, cream the softened butter and 1 cup granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Add half of the dry ingredients to the butter mixture and mix until just combined.
Add the sour cream and mix until smooth.
Add the remaining dry ingredients and mix until just combined, being careful not to overmix.
Fold in the diced apples and chopped walnuts (if using) gently.
Pour the batter into the prepared cake pan and spread evenly.
In a small bowl, mix 2 tablespoons granulated sugar with 1/2 teaspoon ground cinnamon. Sprinkle this mixture evenly over the top of the batter.
Bake for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 15 minutes.
Run a knife around the edges to loosen the cake, then invert onto a wire rack to cool completely before serving.