Preheat your oven to 350F. Grease and flour two 9-inch round cake pans and set aside. Place the sugar and vegetable oil in the standing mixer bowl fitted with a paddle attachment and beat on high speed, scraping down sides of bowl often, until smooth and light, about 4 minutes.
With mixer on low speed, add the eggs, one at a time, scraping down sides of bowl and mixing well after each addition. Add the shredded carrots and mix well. Add the flour, baking powder, baking soda, salt, and cinnamon, and mix until smooth.
Add the pecans and coconut, and mix well. Divide the batter between the prepared pans and bake until the cake springs bake when pressed lightly in the center, 25 to 30 minutes. Let cool for about 10 minutes, then remove the cakes from the pans and let cool completely.
Frosting-Place the cream cheese, butter, powdered sugar, and vanilla extract in a bowl of a mixer fitted with a paddle attachment. Beat on low speed just combine the ingredients, then beat on high speed, occasionally stopping the mixer and scraping down the sides of the bowl, until very light, fluffy, and smooth, about 7 minutes.
To frost place a cake layer (flat side down) on a cake plate, frost top of this layer well. Place second layer (top side down) directly on top of frosted first layer, press gently into the frosting. Frost the sides, filling in as you go and then frost the top of your cake and let frosting set and dry at least 2 hours. Enjoy!