- Make the brine: Bring water to a boil in a large pot. Add salts, sugar, and spices; remove from heat, and stir until salts and sugar dissolve. Let cool.
- Make the corned beef: Place brisket in a nonreactive container just large enough to hold it. Pour cooled brine over meat. Place 2 small plates on top to keep meat submerged; cover, and refrigerate for 2 weeks.
- Rinse brisket; discard brine. Place in a large pot. Add enough water to cover by 2 inches. Add onion, celery, and halved carrot, and bring to a boil. Reduce heat, cover, and simmer until very tender, 3 to 3 1/2 hours.
- Set a steamer in a large saucepan. Add enough water to reach the bottom, and bring to a boil. Add turnips. Reduce heat, cover, and steam until tender, 8 to 10 minutes. Transfer to a bowl. Repeat with baby carrots, steaming 10 to 12 minutes. Add to turnips.
- Transfer corned beef to a cutting board. Tent with foil, and let rest for 30 minutes. Discard remaining solids from broth, then bring to a boil. Add cabbage and potatoes, and simmer until tender, about 25 minutes. Add turnips and carrots, and cook until warmed through. Transfer vegetables to a platter; reserve broth.
- Trim excess fat from beef. Slice thinly against grain, and transfer to platter. Serve with broth and mustard.
Cook's Note: On "Cooking School", Martha added 12 sprigs of fresh flat-leaf parsley. If you would like to use parsley, simply add it in step five along with the cabbage and potatoes. Pink curing salt develops flavor. The brisket can be made without it, but the result won’t be as intense.
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