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1
Preheat oven to 350u00b0 F and position a rack in the center of the oven. Butter two 8-inch cake pans and line them with parchment paper. Butter the paper too, then dust the pans with flour.
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2
Add the beet puree, buttermilk, vinegar, lemon juice, and vanilla extract to a food processor fitted with the steel blade and process until very smooth.
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3
Sift the cake flour, cocoa powder, baking powder, cream of tartar, and salt together in a bowl.
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4
In a large bowl, beat the sugar, oil, and butter together until creamy. Add the eggs one at a time, mixing for 30 seconds after each addition.
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5
Alternating, add the flour mixture and beet mixture, beginning and ending with the flour mixture. Divide between the prepared pans and bake until a bake tester inserted into the center of the cake comes out clean, 20 to 30 minutes.
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6
Cool the cakes on a rack for 20 minutes, then invert onto the rack to cool completely.
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7
To make the frosting: Beat the butter and cream cheese together on high speed until fluffy and smooth add the creme fraiche. Turn the mixer to low and gradually add the confectioners' sugar until just combined, then turn the mixer up to medium-high and beat until fluffy and smooth, making sure to stop the mixer and scrape down to the bottom of the bowl so everything is evenly mixed. Add the lemon zest, vanilla extract, and salt.
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8
To assemble the cake: Trim the tops of the cake layers so they are flat, if necessary. Place one layer on a serving plate or pedestal and spread about 1 cup of frosting on top. Top with the second cake layer, then smooth a thin coat of frosting on the outside of the cake. Chill for at least 30 minutes, then cover the cake with a second, heavier coat of frosting to finish.
