Preheat oven to 350˚F.
Grease a 15x10x1-inch pan with butter and then dust it with flour. Set aside. (You can also use an 18x13 baking sheet, but cake won’t be as tall)
In your electric mixer’s bowl add eggs, oil, and sugar; beat until completely smooth.
In a separate mixing bowl combine flour, baking soda, baking powder, cinnamon, salt, and nutmeg; whisk to combine.
Add flour mixture to the egg mixture and beat well, until everything is thoroughly incorporated.
Remove bowl from the mixer and stir in carrots and walnuts.
Pour batter into previously prepared baking pan. Smooth out the top and rap the pan on your kitchen counter to even it out and eliminate any air bubbles.
Bake for 30 to 35 minutes, or until a toothpick inserted in the center of the cake comes out clean.
In the meantime, prepare the frosting.
Combine butter and cream cheese in your electric mixer’s bowl; add vanilla and beat mixture until smooth.
Add lemon zest and sugar, one cup at a time; continue to beat until completely incorporated, fluffy, and smooth.
Remove cake from oven and let cool completely before frosting.
When cake is completely cooled, cover it with prepared frosting.
Sprinkle with walnuts and coconut shavings.
Cut and serve.
Store cake in refrigerator.