Place the brisket in a large pot and add enough cold water to cover the meat by 3 to 4 inches. Add the pickling spice and garlic and bring to a boil. Reduce to a simmer, cover and cook until the brisket is tender enough that a fork slides easily in and out when poked, 2 1/2 to 3 hours. Remove it from the broth and set aside while you cook the vegetables.
Place the beets in a medium saucepan and cover with water. Bring to a boil and simmer until tender, about 35 minutes. Peel and slice.
Strain the beef cooking broth through a fine-mesh sieve and return it to the large pot, discarding the pickling spices and garlic. Bring the broth back to a simmer and add the carrots, onions, parsnips, potatoes and rutabagas. Simmer, uncovered, until the vegetables are fork-tender but not mushy, 25 to 30 minutes. Remove and set aside. Add the cabbage and simmer for 6 to 8 minutes; it should still be firm but slightly wilted. Put the brisket back into the broth to gently warm while arranging the vegetables on a platter.
Trim and discard the fat from the brisket and slice across the grain into 1/4-inch slices. Top the vegetables on the platter with the sliced corned beef. Garnish with parsley and serve with Horseradish Cream Sauce and some broth on the side.
Mix the sour cream, horseradish, mustard, parsley and salt in a large bowl.