Sprinkle the meat liberally with the celery seeds, salt and pepper up to 1 day in advance. Remove the meat from the refrigerator 45 minutes to 1 hour before cooking to take the chill off it. Preheat the oven to 325 degrees F.
Heat a large Dutch oven over high heat. Add a drizzle of olive oil, followed by the brisket. Sear the meat until golden brown and crusty, 3 to 5 minutes on each side. Set aside.
Add the celery, carrots and onions to the Dutch oven, along with a pinch of salt. Brown the vegetables, about 3 minutes, then add the garlic and thyme and cook 1 to 2 minutes longer. Stir in the tomato paste and toast it until it's rust colored, 1 to 2 minutes.
Add the wine to deglaze the pot, scraping up the browned bits on the bottom. Add the meat back in, then add enough stock to cover the roast halfway. Bring the liquid to a simmer and taste for seasoning, adding more salt if necessary. Cover and roast in the oven, basting the meat occasionally, until the roast is tender, 3 to 4 hours.
If you're serving individual plates, the meat can be removed to a cutting board and sliced. Or, the meat can be pulled apart with a couple of forks right in the pot at the table and served with plenty of the sauce and vegetables.