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In a medium saucepan over high heat, combine the carrots and enough water to cover. Bring to a boil, then reduce heat to maintain a simmer, and cook until the carrots are tender, 10 to 15 minutes.
Drain the carrots and transfer to a food processor. Process until smooth. (Alternatively, a potato masher can be used to make the purée, however, it will have a coarser consistency.)
Preheat the oven to 350°F (175°C). Adjust the oven rack to the center position and butter two 9-inch round cake pans or, in a pinch, springform pans. If desired, line the pans with parchment paper cut to fit.
In a large bowl, combine the flour, sugar, salt, baking soda, and cinnamon. Add the oil, eggs, and vanilla. Beat well. Fold in the walnuts, coconut, carrots, and pineapple. The batter will be quite thick.
Scrape the batter into the prepared pans. It may come close to the top. This is fine. Bake until the edges have pulled away from the sides and a cake tester inserted in the center comes out clean, 50 to 60 minutes.
Cool the cakes in the pans, on a wire rack for 3 hours. Remove the parchment, if using.
In a stand mixer or a large bowl with a handheld electric mixer, beat the cream cheese and butter until well combined and almost fluffy, 2 to 3 minutes. Your cream cheese and butter MUST be at room temperature, as noted in the ingredients list, to ensure a lumpless frosting.
Slowly, slowly sift in the confectioners' sugar and continue beating until fully incorporated, which could take anywhere from 1 1/2 to 4 minutes. The mixture should be free of lumps.
Stir in the vanilla, and lemon juice if desired.
Place the bottom layer of the cake on a serving platter. Spread a layer of frosting over the cake, then carefully top with the second cake. Frost the top and sides of the cake with the remaining cream cheese frosting. (You can stash any leftover cake in the freezer and it will keep magnificently for up to 3 months.)