Prepare your vegetables: chop the onion, the carrots, and the celery. Aim for 1″ pieces.
Set the rack in your oven to the lower third, and heat your oven to 350°.
In a large, oven-safe pot, heat the oil over medium-high heat until it gets shimmery. Rub both sides of the brisket with salt and pepper (about 1 tsp of each), and brown it in the pot, turning it once. Remove the browned brisket to a plate.
Reduce the heat to medium. Add the onions to the pot and cook them until they turn golden-brown (about 12-15 min). Add in the carrots, celery, and garlic, and cook for another 10-12 min, stirring occasionally. Add the wine or beer, stirring well and scraping up the yummy bits from the bottom of the pot.
Add the chicken stock and tomatoes, and bring the pot to a simmer.
Return the brisket to the pot (the liquid almost certainly won’t completely cover the brisket. Don’t worry, it’s not supposed to). Cover the pot with a tight-fitting lid, stick it in the oven, and braise it for about 3 to 3 1/2 hours (until it’s fork tender).