I actually made this using the liquid from 2 cans of beets. These were plain canned beets NOT pickled beets. Canned beets are generally just beets, water and salt (you can sometimes find beets canned in water-only). Some of the beet nutrients and flavors leech into the canning water, making canned beet liquid a by-product worth saving.
I had been saving this liquid for a couple of weeks (although I've read you should use it within about 1 week), waiting for an opportunity to use it. One day last week, the cold and rainy weather motivated me to make a nice soup for the 4 of us, using up the beet liquid. In addition to the beet liquid, I used half of a small onion, a small carrot, a bit of vegetable oil, potato flakes, and chicken bouillon.
I cooked the diced onions and carrots in the vegetable oil until translucent, then added the beet liquid and a little water, cooking until the veggies were soft. Next, I stirred in enough potato flakes to thicken and the bouillon to flavor. That was it. It came out creamy and lightly beet-flavored. This was such a hit with my daughters that they've agreed to save the liquid from cans of beets that they buy for themselves (yes, they like canned beets that much, they'll buy some just for themselves).
Just another way to use a food by-product that might otherwise be tossed out.