Naturally-Dyed Red Velvet Cake with Cream Cheese Frosting

Makes: an 8-inch cake with two layers or 24 standard cupcakes

For the cake:

• 1 cup beet purée, from fresh red beets (not cooked; chop & puree in food processor)
• 3/4 cup buttermilk
• 1 tablespoon white wine vinegar
• 2 tablespoons lemon juice
• 1 tablespoon vanilla extract
• 2 1/2 cups cake flour (make cake flour by 1C - 2T regular flour + 2T corn starch)
• 3 tablespoons cocoa powder, not Dutch-process
• 2 teaspoons baking powder
• 1 teaspoon cream of tartar
• 1 teaspoon salt
• 1/2 cup neutral-flavored oil
• 1/2 cup unsalted butter, softened
• 2 cups granulated sugar
• 3 large eggs

Directions:

1. Preheat oven to 350° 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.
2. Add the beet purée, buttermilk, vinegar, lemon juice, and vanilla extract to a food processor fitted with the steel blade and process until very smooth. 
3. Sift the cake flour, cocoa powder, baking powder, cream of tartar, and salt together in a bowl. In a large bowl, beat the sugar, oil, and butter together until creamy. 
4. Add the eggs one at a time, mixing for 30 seconds after each addition. Alternating, add the flour mixture and beet mixture, beginning and ending with the flour mixture. 
5. 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. Cool the cakes on a rack for 20 minutes, then invert onto the rack to cool completely.
6. For cupcake: Bake for 20 to 25min for regular size cupcakes

Note: The acid and uncooked beets is  necessary for the red color to stay in cake

For the cream cheese frosting:

• 8 ounces cream cheese, at room temperature
• 8 ounces unsalted butter
• 2 tablespoons crème fraîche
• 1 pound confectioners' sugar
• 1/2 teaspoon lemon zest (or 1/4 teaspoon lemon extract)
• 1 teaspoon vanilla extract
• 1 pinch salt

Directions:

1. Beat the butter and cream cheese together on high speed until fluffy and smooth
2. Add the crème fraîche. 
3. 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. 
4. Add the lemon zest, vanilla extract, and salt. 

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.

From: https://food52.com/recipes/40622-naturally-dyed-red-velvet-cake-with-cream-cheese-frosting