Preheat the oven to 325F.
Season the brisket with salt and pepper on all sides. Set aside.
Heat the butter and the oil in a braising pan over medium-high heat. Add the brisket and sear for about 4-5 minutes per side, or until a light-brown crust appears. Move the brisket to a large cutting board and let rest.
In the same pan, lightly brown the onions and the garlic over medium-high heat, about 4-5 minutes. Add a tablespoon of butter if necessary.
Add the flour and continue cooking while constantly stirring for about 30 seconds.
Add the beef broth, bring to a simmer and deglaze the pan, scraping the brown bits from the bottom using a flat wooden spatula. Continue simmer until the mixture thickens.
Add the vinegar, thyme and oregano and stir. Taste for salt. Adjust if needed. Turn off the heat.
Slice the brisket about 1/2" thick across the grain. Slide off to the braising pan. Spoon the gravy, onions and sliced garlic all over the meat. Top with two bay leaves, cover with the lid and transfer to the preheated oven.
Cook at 325F for 4 hours.
Serve hot with your favorite side dish. Spoon pan juices/gravy over the meat and the side, e.g. mashed potatoes. Garnish with finely chopped parsley.