Spray two 8- or 9-inch round cake pans with non-stick cooking spray, and line the bottom of the pans with parchment paper.
Place chocolate chips in a microwave-safe bowl and microwave on half-power for 1 1/2 minutes or until melted. Stir until smooth and set aside.
Combine gluten-free flours, cocoa powder, baking powder, xanthan gum, baking soda and salt in a large bowl. Whisk together with a fork.
Pour a jar of borscht into blender. Puree thoroughly to incorporate any bits of beet. Measure 1 1/2 cups of pureed borscht and set aside.
Preheat oven to 350 degrees. Beat sugar and eggs until pale yellow, using an electric mixer at medium-high speed. Beat in oil and vanilla extract. Mix in melted chocolate and scrape down sides of bowl. Lower speed and gradually beat in flour mixture. Pour in pureed borscht and mix on low speed for 1 minute, scraping the sides and bottom of the bowl.
Pour batter into prepared pans. Bake at 350 degrees for 28 to 30 minutes, or until top is springy and cake tester inserted into the middle of the cake comes out clean.
Cool cake in pans for 10 minutes. Then invert cakes onto wire rack, remove parchment paper and cool completely before frosting.
To make Pink Buttercream Frosting, combine confectioners’ sugar, butter, borscht and vanilla extract in the bowl of an electric mixer. Start at low speed and gradually increase to high speed, beating for 3 minutes until frosting is smooth and fluffy. (If frosting is too thick, beat in a little bit of milk or water.)
To frost, place one layer of the cake on a serving plate, with the rounded side down and the flat side facing up. Spread Pink Buttercream Frosting on the flat side of the cake. Top with another layer of cake (flat side down, round side up). Frost the top and sides of the assembled cake.