Bring two gallons of water to a boil in a large stockpot.
Trim all huge slabs of fat from the brisket, but don't be too severe about this. Cut it if necessary into two or three pieces to fit your pot. (It's okay if it sticks out a little bit.) Put it into the water (no need to wait for it to boil). Add all the other ingredients. Cover the pot.
When the pot comes to a boil, lower it to the lowest possible temperature. Simmer for four to six hours, or whatever it takes for the brisket to pull apart when clutched with tongs. Skim off the scum that may rise to the surface.
Remove the brisket and set aside. Strain out the vegetables and discard, but save the beef stock for other uses--notably vegetable soup. The stock can be kept in the refrigerator for about a week, or it can be frozen almost indefinitely.
Slice the brisket it or serve it in large cubes, but cut against the grain with a sharp, non-serrated knife. The meat will be falling apart and easy to eat. Serve with boiled cabbage, potatoes, and carrots.
To make the sauce, blend the three sauce ingredients. Serve cool.