Preheat oven to 350℉.
To prepare cake, lightly spoon flour into dry measuring cups; level with a knife.
Combine flour, sugar, coconut, pecans, baking soda, salt, and cinnamon in a large bowl; stir well with a whisk.
Combine oil and eggs; stir well.
Stir egg mixture, grated carrot, and pineapple into flour mixture.
Spoon batter into a 13 x 9-inch baking pan coated with cooking spray.
Bake at 350°F for 35 minutes or until a wooden pick inserted in the center comes out clean.
Cool completely on a wire rack.
To prepare frosting, combine butter and cream cheese in a large bowl.
Beat with a mixer at medium speed until smooth.
Beat in powdered sugar and vanilla just until smooth.
Spread frosting over top of cake.
Garnish each serving with grated carrot, if desired.