Cut the cooked beetroot into small cubes. Sauté the onion and garlic in hot butter. Add beetroot, vegetable stock and horseradish. Cook for 15 minutes in a closed saucepan.
Puree the soup. Stir in sour cream (hold back 1 tablespoon), season with pepper, salt and sugar. Serve the beetroot cream with a dollop of sour cream and basil.