Place water, salt, carrots, 1/2 of the bell pepper, celery, beet, tomatoes, and quartered potatoes in a large stock pot over high heat. Bring to a boil.
Melt 1/3 cup butter in a separate skillet over medium heat. Saute onions in butter until tender, approximately 5 minutes. Stir in tomatoes, reduce heat to medium low, and simmer for 15 minutes. Remove 1/2 cup of sauce from skillet, and set aside. Stir half of the cabbage into the skillet with remaining sauce, and continue simmering 5 minutes more, or until tender.
Remove beet from boiling liquid and discard. Remove potatoes with a slotted spoon or tongs, and place in a bowl with remaining 1 tablespoon of butter and the cream. Mash together until smooth.
Return the 1/2 cup of reserved onion-tomato sauce to the stock pot. Stir in diced potatoes, and simmer until just tender but still firm, approximately 5 minutes. Increase heat to a low boil, and stir in remaining cabbage, tomato sauce, and mashed potatoes. Reduce heat and simmer a few minutes more. Stir in remaining bell pepper, season with black pepper, and serve.