FOR THE BEEF STOCK: Combine the beef brisket and 2 quarts of cold water in a heavy 4 to 5 quart enameled or stainless steel casserole. Bring to a boil over high heat, meanwhile skimming off the foam and scum as they rise to the surface. Add the bacon, onion, parsnip, carrot, garlic, parsley root, bay leaf, 1 teaspoon salt and a few grindings of pepper. Then reduce the heat to low and simmer partially covered for about 2 hours, or until the brisket is tender and shows no resistance when pierced deeply with the point of a small skewer or knife.
With tongs or a slotted spoon, transfer the brisket to a plate and drape foil over it to keep it warm.
Strain the contents of the casserole through a fine sieve into a deep bowl, pressing down hard on the bacon bits and vegetables with the back of a spoon to extract all their juices before discarding them. With a large spoon, skim off and discard as much of the surface fat as possible. Return the stock to the casserole.
FOR THE BEET STOCK: In a 3 to 4 quart enameled or stainless steel saucepan, bring the grated beets and 5 cups of cold water to a boil over high heat. Reduce the heat to moderate and cook uncovered for 10 minutes. Then reduce the heat to low, stir in the vinegar and 1 teaspoon of the salt, and simmer, partially covered, for 30 minutes. Strain the stock through a fine sieve into a glass or ceramic bowl, pressing down hard on the beets with the back of a spoon to extract all their juice before discarding them.
The beet and beef stocks may be set aside at this point if you wish to use the brisket to make meat stuffed buns (Ukrainian Filled Yeast Pyrizhky (Stuffed Buns with Variations) see recipe, usually accompanying the soup.
Just before serving, combine the stocks, add the remaining 1/2 teaspoon of salt, the lemon juice and sugar, and bring to a boil over high heat. Taste for seasoning and serve at once from a heated tureen or individual soup plates. If you have not prepared the pyrizhky, the brisket may be sliced and served with the soup. Serves 8 to 10.