Preheat your oven to 350°F (180°C). Grease and line an 8-inch round cake pan.
In a large bowl, whisk together flour, cinnamon, nutmeg, baking powder, and baking soda.
In another bowl, whisk sugar, oil, and eggs until well combined.
Stir the wet ingredients into the dry ingredients until just combined.
Fold in the grated carrot, grated apple, and nuts if using.
Pour the batter into the prepared pan and smooth the top.
Bake for 45–50 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely.