Place brisket in a large plastic, glass, or stainless steel container with a tight-fitting lid; cover with water. Add remaining ingredients, stirring until salt dissolves. Cover and marinate 21 days in the refrigerator, turning meat occasionally.
Remove brisket from marinade; discard marinade.
Place brisket in a large Dutch oven with water to cover. Bring to a boil. Reduce heat; cover and simmer 2 1/2 hours. Remove from heat; let stand, without removing cover, for 2 hours.
Remove brisket from cooking liquid; discard cooking liquid. Rinse brisket in cool water; drain. Firmly press entire surface of brisket to remove remaining cooking liquid. Cover and refrigerate.
Cut corned beef diagonally across the grain into thin slices for sandwiches or follow specific recipe directions for preparing corned beef.