Preheat oven to 350°F (175°C). Grease and line two 9-inch round cake pans with parchment paper.

1. In a large bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
2. In another bowl, beat eggs, granulated sugar, brown sugar, oil, and vanilla extract until smooth.
3. Stir grated carrots, shredded coconut, and nuts (if using) into the wet mixture.
4. Add the wet ingredients to the dry ingredients and mix until just combined.
5. Divide batter evenly between prepared pans and bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean.
6. Cool cakes in the pans for 10 minutes, then turn out onto a wire rack to cool completely.
7. To make the frosting, beat cream cheese and butter until smooth and creamy. Gradually add powdered sugar and beat until fluffy.
8. Place one cake layer on a serving plate, spread with frosting, top with the second layer, and frost the top and sides of the cake.
9. Decorate with extra shredded coconut or chopped nuts if desired. Chill before slicing for clean cuts.