Preheat the oven to 325 degrees F and adjust a rack to the lower third of oven.
Remove the brisket from the refrigerator and let rest for 1 hour to come up to room temperature.
Pat the brisket dry and sprinkle it generously on both sides with salt and pepper. Heat the oil in a Dutch over or braising pot set over medium-high heat. Sear the brisket in the oil until well browned, about 4 minutes. Carefully flip and sear on the reverse side for another 4 minutes. Remove the brisket to a plate.
To the pot, add the garlic, onions, carrots, celery, thyme, rosemary and bay leaf. Saute until golden, about 8 minutes. Stir in the tomato paste and cook for 2 minutes. Add the vinegar, chicken stock and beer, and bring to a simmer, scrapping up any bits that are stuck to the bottom of the pan.
Nestle the brisket into the pot, making space between the vegetables, and cover with a tight-fitting lid. Place in the oven and cook for 3 1/2 hours, or until fork tender. Let rest for 15 minutes before slicing thinly against the grain.
Serve on a platter along with the vegetables and any extra braising liquid as a sauce.
Recipe courtesy of Nancy Fuller