Preheat the oven to 350°F (175°C). Grease and flour a 9×9 inch baking pan or a similar sized round cake pan.
In a large mixing bowl, combine the yellow cake mix, ground cinnamon, and ground nutmeg. Stir to evenly distribute the spices throughout the mix.
Add the vegetable oil, eggs, water, and vanilla extract to the dry ingredients. Mix well with a hand mixer or whisk until smooth and well combined.
Fold in the diced apples and chopped walnuts (if using) gently until they are evenly distributed in the batter.
Pour the batter into the prepared baking pan and spread it out evenly.
Sprinkle the granulated sugar evenly over the top of the batter to create a slightly sweet crust.
Bake in the preheated oven for 35 to 40 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 on a wire rack for at least 15 minutes before serving.
Slice and serve warm or at room temperature. Optionally, dust with powdered sugar or serve with whipped cream.