For the Corned Beef:
1/2 cup kosher salt
1 tablespoon cracked black peppercorns
1 tablespoon dried thyme
2 1/4 teaspoons ground allspice
1 1/2 teaspoons paprika
2 bay leaves, crumbled
1 (4- to 5-pound) beef brisket, flat cut, trimmed
For the Vegetables:
1 1/2 pounds carrots, peeled and halved crosswise, thick end halved lengthwise
1 1/2 pounds small red potatoes
1 rutabaga (1 pound), peeled and halved crosswise; each half cut into 6 chunks
1 small head green cabbage (2 pounds), uncored, cut into 8 wedges
For the Corned Beef: In a small bowl, combine salt, peppercorns, thyme, allspice, paprika, and bay leaves.
Using metal skewer, poke 30 holes on eachside of the brisket. Rub each side evenly with the salt mixture. Place brisket in 2-gallon zipper-lock bag. Try to force out as much air as possible.
Place in 13 by 9-inch baking dish, cover with second, similar-size pan, and weight with 2 bricks or heavy cans of similar weight (about 12 pounds). Refrigerate 5 to 7 days, turning once a day.
Remove the brisket from the brine and rinse off the brine with cold water. Pat the brisket dry with paper towels. Place the brisket in a large Dutch oven and cover with 1 inch of water. Bring to boil over high heat. Reduce heat to medium-low, cover, and simmer until skewer inserted in thickest part of brisket slides in and out with ease, 2 to 3 hours.
Adjust oven rack to middle position and heat oven to 200 degrees. Transfer meat to large platter, ladle 1 cup cooking liquid over meat, cover with aluminum foil and place in oven to keep warm.
For the Vegetables: Add carrots, potatoes, and rutabaga to the remanning cooking liquid in the Dutch oven and bring to a boil over high heat. Reduce heat to medium-low, cover, and simmer until vegetables begin to soften, about 7 minutes.
Add cabbage, increase heat to high and return to boil. Reduce heat to medium-low, cover, and simmer until all vegetables are tender, 13 to 18 minutes.
Meanwhile, remove meat from oven, transfer to a carving board, and slice against grain into 1/4-inch slices. Return meat to platter. Transfer vegetables to meat platter, moisten with additional broth. Serve with horseradish, either plain or mixed with whipped cream or sour cream, or with grainy mustard.