Cook beets by steaming them or boiling slowly until they're fork-tender through to their centers (about 15 minutes). Allow to cool. Run under cool water and rub off the peel. Cube into approximately 3/4" cubes. Spread beets onto parchment lined cookie sheet and freeze, 6 hours minimum or overnight. (If making ahead, gather up frozen cubes and place in freezer storage container until you're ready to use.)
Place frozen beets into high-powered blender. Add maple syrup, fresh ginger, and vanilla. Add 2 cups milk of choice. Process on medium speed until the chunks are smaller and blender stops because it needs more liquid.
Add cream, release air bubble by blade, and process again on high speed until milkshake/smoothie is totally smooth, about 25 seconds.