Preheat the oven to 350 degrees F. Pat the brisket until very dry and sprinkle liberally with salt and pepper. Heat the oil in a large Dutch oven over medium-high heat, and then brown the meat well on all sides, 10 to 12 minutes. Transfer to a large plate and set aside.
Combine 1/4 cup of the beef stock, the celery, carrots, bay leaves, onions and thyme in the same Dutch oven and cook until the vegetables have started to brown and soften slightly, 4 to 6 minutes. Pour in the beer, bring to a boil and cook until reduced by half, 2 to 3 minutes. Return the brisket to the Dutch oven, and then pour in the remaining beef stock. The brisket should be at least halfway covered by the liquid.
Cover the pot and transfer to the oven for 3 hours 30 minutes. Remove the lid and cook uncovered for another 30 minutes. Let the brisket rest in the liquid in the pot for 20 minutes before transferring to a cutting board.
To serve, slice the brisket against the grain, place on a platter and ladle some braising liquid on top.