Make the cake.  Preheat oven to 350 degrees F.  Oil two 8 or 9 inch round cake pans.

In a high powered blender, puree the beets with ¼ cup water until completely smooth.  Measure out 2 cups of the beets for the cake and save the rest for another use.

In a large bowl, whisk together eggs, sugar, and oil until combined and lightened in texture, about 5 minutes.  A hand or stand mixer would also work, but I like the challenge.  Gently stir in the beet puree, followed by the flour, baking powder and soda, and the grated chocolate or carob.

Divide batter evenly between the prepared pans and bake about 25 minutes until a toothpick inserted in the center comes out clean or with a few moist crumbs.  Allow cakes to cool completely in pans.

Make the frosting.  In a high powered blender (I did the beets at the same time with a quick rinse in between), place the cashews, milk, syrup, and lemon.  Blend until completely smooth, using a tamper if your blender has one.  Pour into a bowl.  Stir in the vanilla and carob or cocoa powder until well incorporated.  Refrigerate overnight for best results to allow to set.

Assemble the cake.  Cut each of the cake layers in half horizontally.  Place one layer on a cake plate or stand.  Top with frosting, spread into an even layer.  Top with cake, and more frosting.  I added some chopped carob on this middle frosting layer, a totally optional step that just adds a little something extra.  Feel free to use dark chocolate if you choose.  Cake, frosting, cake, and the rest of the frosting on top.  I used an offset spatula to make a swirl pattern and sprinkled with some grated carob.  Serve immediately or store in an airtight container in the refrigerator for up to 3 days.  Cake may also be frozen, wrapped in plastic and foil and placed in a zipper bag for up to 3 months.  Thaw in the refrigerator overnight.