Heat olive oil in a large heavy stockpot over medium heat. Add onion, garlic, and celery. Cook until light brown, stirring occasionally, about 10 minutes.
Add tomato juice, 5 cups water, potatoes, and wine. Bring to a boil. Reduce heat to a simmer, and cook 5 minutes. Add thyme, celeriac, carrots, fennel, chopped tomatoes, reserved juice, and Parmigiano-Reggiano rind; stir well to combine. Cook until vegetables are fork tender, 15 to 20 minutes.
Stir in escarole and parsley. Cook until escarole wilts. Season, to taste, with salt and pepper.
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