Heat oven to 350° F. Butter two 9-inch round cake pans and line the bottom of each with a round of parchment paper.
Combine grated beets and sugar in a large bowl. Stir well and set aside for 10 minutes to let sugar dissolve. In another bowl, whisk together the flour, cocoa powder, cinnamon, and baking soda.
Add the oil, sour cream, eggs, vinegar, and vanilla to the beet mixture and stir to combine. Gradually add the flour mixture to the beet mixture, then stir until just combined.
Divide the batter evenly between the prepared pans. Bake until a toothpick inserted in the center of each cake comes out clean, 35 to 45 minutes. Cool in the pans for 20 minutes, then turn out onto a rack to cool completely.
Make the frosting: Using a hand mixer or an electric mixer fitted with the paddle attachment, cream the butter and apple butter in a large bowl until soft, about 1 minute. With the mixer on low, gradually add the sugar. When all the sugar has been incorporated, add the cream. Increase mixer speed to high and cream the ingredients until light and fluffy, about 4 minutes.
To assemble, transfer one of the cakes to a platter or cake stand and spread with a thin layer of frosting. Top with the remaining cake and cover the cake with the remaining frosting. If you want an extra bit of sparkle, sprinkle the edges of the cake with turbinado sugar.
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