Wise journalists, students and trivia contestants know not to trust Wikipedia unthinkingly. There is no better support for this rule of thumb than the open-source encyclopedia's entry for carrot cake, which currently begins:
"Carrot cake is a cake or pie which contains carrots mixed into the batter. The carrot softens in the cooking process, and the cake usually has a soft, dense texture. The carrots themselves do not enhance the flavor, texture and appearance of the cake."
The misinformation contained in these three sentences boggles the mind. Carrot cake is self-evidently not a pie. Carrots absolutely enhance the flavor of carrot cake -- it's not like all their flavor compounds evaporate while the cake is baking. Furthermore, as sentence No. 2 of the above paragraph attests, they affect the texture, too, lending the batter moisture and body. Carrots also quite obviously enhance the appearance of cake, assuming you consider bright, cheerful orange specks to be a visual enhancement. (I do, and freckle fetishists the world over agree with me.) To assert that the "carrots themselves do not enhance the flavor, texture and appearance of the cake" is to inadvertently raise all sorts of troubling questions about the nature of perception and existence. (If a carrot falls into a cake batter and no one is around to taste it …)
Anyway, Wikipedia's diligent volunteer editors are clearly mistaken about carrot cake, which is a great foodstuff, and which needs carrots the way Ben Folds Five needs Ben Folds.
It needs other things, too, to be sure: Spices, like cinnamon, cloves and allspice, to offset the earthiness of the carrots. Shredded coconut, with its savory edginess, adds another flavor dimension. (Walnuts are optional, and raisins do not belong in any cake that is not explicitly a fruitcake.)
And then there is the most important component: the cream cheese frosting. I don't know why cream cheese frosting isn't standard on more cakes. Properly made, it's devastatingly tangy and sweet, unlike plain buttercream frosting.
Yield: 16 to 20 servings; Time: 1½ to 2 hours, partially unattended
Oil or butter for greasing the pan
2 cups all-purpose flour
½ cup unsweetened shredded coconut
½ cup chopped walnuts (optional)
1½ teaspoons baking powder
½ teaspoon salt
1 teaspoon ground cinnamon
¼ teaspoon ground cloves
¼ teaspoon ground allspice
1 cup (2 sticks) unsalted butter, softened
½ cup canola or grapeseed oil
1½ cups brown sugar
4 large eggs
1 tablespoon plus 2 teaspoons vanilla extract
8 ounces grated or shredded carrots (about 3 loosely packed cups)
8 ounces cream cheese, softened
2 cups powdered sugar
Heat the oven to 350 degrees and grease a 9-by-13-inch pan. Put the flour, coconut, walnuts (if desired), baking powder, salt, cinnamon, cloves, and allspice in a large bowl and stir to combine. Beat ¾ cup (1½ sticks) butter, the oil, and the brown sugar with the paddle attachment of a stand mixer (or with a handheld mixer) until light and fluffy. Add the eggs and 2 teaspoons vanilla extract and beat for 2 minutes. Gently stir in the flour mixture, then fold in the carrots. Transfer the batter to the greased pan and bake until a knife inserted into the center of the cake comes out clean, 30 to 40 minutes. Cool the cake.
Beat the remaining ¼ cup (½ stick) butter and the cream cheese with the paddle attachment of a stand mixer (or with a handheld mixer) until well combined. Add the powdered sugar and beat on low speed to combine, then add the remaining 1 tablespoon vanilla. Beat for at least 10 minutes.
Spread the frosting on the cake and serve. (Store leftover cake in an airtight container at room temperature for up to a few days.)