Preheat oven to 350°. In a small bowl, mix together ground flaxseed and water. Set aside.
Make your beet puree. Wash 2 medium beets, then cut off the ends. Peel them with a vegetable peeler or paring knive until entire skin is removed. Using a stain-proof cutting board and gloves, cut the beets into ½ inch cubes and add to the food processor along with ½ cup of water. Pulse and puree for several minutes, until smooth.
In a large bowl, mix together ¾ cup beet puree, melted coconut oil, avocado oil, vinegar, lemon juice, vanilla, flaxseed mixture, and buttermilk until well combined. Stir in the sugar until dissolved.
Add the flours, cocoa powder, salt, baking powder, baking soda, and cream of tartar. Whisk until just combined.
Pour the batter into 2 greased, 9 inch cake pans, or 12 lined cupcake molds. Bake in the preheated oven for 24-26 minutes (for cake) or 20-22 minutes (for cupcakes).
Meanwhile, make the frosting. In a medium bowl, beat together the softened cream cheese, water, powdered sugar, and vanilla until smooth and creamy. Set aside.
After your cake is done baking, allow to cool completely. Frost, then serve!