Preheat your oven to 300°F (150°C).
Season the beef brisket generously with salt and pepper.
Heat olive oil in a large oven-proof pot over high heat. Add the brisket and sear each side until browned, about 3-4 minutes per side. Remove the brisket from the pot and set aside.
In the same pot, reduce the heat to medium. Add onions and garlic, sautéing until softened, about 5 minutes.
Pour in red wine to deglaze the pot, scraping up any browned bits from the bottom. Allow to simmer and reduce by half, about 4 minutes.
Return the brisket to the pot. Add beef broth, carrots, celery, bay leaves, and thyme. Bring to a simmer.
Cover the pot with a lid and transfer to the oven. Cook for about 4 hours or until the meat is tender and falls apart easily with a fork.
Remove the brisket from the pot and let it rest for 10 minutes before slicing. Serve with the vegetables and sauce from the pot.