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When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 350F and preheat, lid closed, for 10 to 15 minutes.
If your butcher has not already done so, trim the fat cap on the brisket to 1/4-inch. Season generously with the Traeger Prime Rib Rub. Distribute the onions, garlic, carrot, and celery evenly on the bottom of a large roasting pan. Whisk the tomato paste, Worcestershire sauce, and thyme into the wine and pour over the vegetables. Add the tomatoes and beef broth, and bury the bay leaves in the vegetables.
Lay the brisket fat-side up on top of the vegetables. Cover tightly with aluminum foil. Arrange the roasting pan on the grill grate and braise the meat for 3-1/2 to 4 hours, or until the meat is fork-tender. (Halfway through the cooking time, carefully lift the foil and turn the meat over. Replace the foil.)
Let the brisket rest for 30 minutes. Remove and discard the bay leaves from the vegetables and skim any visible fat from the liquids. Transfer the brisket to a cutting board and slice into 1/4-inch slices.
If desired, puree the vegetable sauce in batches in a blender jar. (Do not fill the jar over halfway, and hold a thick towel firmly over the lid as you process the mixture. Steam can cause the lid to pop off.) Spoon over the sliced meat and top with parsley, if desired. Please note: The brisket can be cooked up to 2 days in advance and refrigerated. (Discard any fat that congeals around the brisket or on top of the sauce.)
Reheat, covered tightly with foil and moistened with sauce, for about an hour at 350F.