Remove the stems from the beets, but don't peel. Cover them with water in a large saucepan. Bring to a boil, then reduce to a simmer and cook for 30 to 40 minutes.
Remove from heat. Spoon out the beets and set them aside to cool. Transfer 1 cup of the beet cooking liquid to a smaller saucepan. (Reserve the remaining liquid.) Add the barley (or oats) and cook over medium heat for about 20 minutes, until all the liquid is absorbed. Remove from heat and let cool.
Peel the cooked beets and cut them into quarters. Using a blender or food processor, purée the beets with the barley, brown sugar, and lime (or lemon) juice. Add enough of the reserved beet liquid to thin slightly.
Pour the purée into a saucepan or soup pot. Add the buttermilk (or yogurt). Heat the soup thoroughly, but do not allow it to boil. Add salt and pepper to taste. Thinly slice the white parts of the scallions. Garnish each serving with a dollop of the sour cream (or yogurt) and a sprinkling of the scallions.
To cut some calories, substitute plain yogurt for both the buttermilk and the sour cream in this recipe.