Preheat the oven to 375°. Wrap the beets in 2 sheets of heavy-duty foil. Set the packages on a baking sheet and roast the beets for 1 1/2 hours, or until they are tender. Let cool in the foil.
Meanwhile, peel the parsnips, carrots and celery root; cut into 1/4-inch dice. In a large skillet, melt the butter in the water. Add the diced vegetables and cook over moderate heat until almost tender, about 8 minutes. Season with salt and white pepper and remove from the heat.
Peel and quarter the beets. Working in batches, in a blender, puree the beets and stock until very smooth. Transfer to a large saucepan. Stir in the vinegar; season with salt, white pepper and green Tabasco. Add the vegetables and simmer over moderate heat for 5 minutes before serving.