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Place brisket in 6-quart saucepot or Dutch oven. Cover with about 2 quarts water. Add onion, pickling spice and garlic; cover.
Bring just to boil. Reduce heat to low; cover and simmer 2 hours. (Do not boil.) Add potatoes and carrots; simmer 30 minutes longer. Add cabbage; simmer 15 minutes longer. Remove brisket and vegetables from saucepot.
Slice brisket across the grain. Mix butter and parsley; brush on vegetables.