Preheat the oven to 350 degrees F. Grease and flour a bundt pan or two 9-inch round pans and set aside for later.

In a large mixing bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon. Set to the side.

In a separate bowl, whisk together the eggs, yolk, and sugars. Blend until well incorporated. Carefully whisk in the oil. Add the crushed pineapple and vanilla. Mix until well incorporated.

Add the pineapple mixture to the flour mixture all at once. Fold together with a spatula. When just about incorporated, add in the carrots, coconut, and walnuts. Fold together.

Pour the batter into the greased pan. If using a round pan, bake for 35 to 45 minutes. If baking in a bundt pan, bake for 45 to 55 minutes. Bake cake until a toothpick inserted into the center comes out clean.

Let cake cool in pan for fifteen minutes, then invert and transfer to wire rack to finish cooling completely.

While the cake cools, make the frosting. In the bowl of an electric stand mixer, fitted with the paddle attachment, beat the cream cheese on medium speed for about three minutes.

Scrape down the sides of the bowl, add the butter, and beat for another two minutes until combined.

Scrape down the sides and add the sifted powdered sugar followed by the vanilla. Beat together on low until all the powdered sugar is incorporated and the frosting is velvety.

Spread over carrot cake and serve.