Heat oil in a large Dutch oven over medium-high heat. Add onion, carrot, and celery; sauté 5 minutes or until tender, stirring frequently. Stir in beets and next 6 ingredients (beets through tomatoes). Bring to a boil; reduce heat, and simmer 35 minutes or until vegetables are tender. Stir in beet greens and sugar; cook 5 minutes.
Add the greens to the soup at the end for a nutritious boost. If you prefer, you can use less than the four cups of beet greens called for in the recipe.