After 7-10 days, remove the brisket from the brine and discard brine.
Thoroughly rinse the brisket to remove salt from the exterior of the meat.
Place brisket in a Dutch oven or pot large enough to hold the brisket and enough cold water to cover the meat.
Bring the water to a simmer.
(Optional step: To reduce saltiness of the brisket, you can remove pot from the heat and discard the water. Then, refill the pot with cold water and bring it back up to a simmer.)
Add the pickling spices and bring to a boil. Cook for 20 minutes. Skim off any foam or residue that accumulates on the surface.
Reduce heat to a simmer and cook for 3-4 hours until tender. (As a guideline, suggested cooking time is 45 minutes per pound of meat.)
Approximately 30 minutes before the meat is done, add the potatoes and carrots.
Approximately 15 minutes before the meat is done, add the cabbage.
Remove corned beef and vegetables from the cooking water.
Slice meat diagonally across the grain. Serve with cooked vegetables.