Lay the brisket on a clean work surface or cutting board. Using the tip of a knife, cut small slits over the surface of the fatty side. Season the brisket liberally with the salt and pepper. Let the meat stand for 30 minutes at room temperature.

Meanwhile, peel the onion and carrots. Slice the onion into 3/4-inch half-moons, and slice the carrots on a diagonal into 1-inch pieces. Peel and smash the garlic cloves.

Preheat the oven to 300°F.

Set a large Dutch oven over medium-high heat and add the oil. When oil is shimmering, carefully place the brisket, fat side down, into the pot. Sear without moving until deeply browned on the bottom, 3-4 minutes. Flip brisket and sear on the opposite side, 3-4 minutes.

Transfer the brisket to a large platter.

Reduce heat under Dutch oven to medium. Add the onion, carrots, garlic, and herbs. Cook, stirring occasionally, until onion is slightly softened, 4-5 minutes. Pour the beef broth into the pot, scraping up any browned bits from the bottom. Stir in the vinegar and ketchup.

Place the brisket, fat side up, on top of the vegetables. Pour any drippings from the platter into the pot. Bring the liquid to a simmer, then remove pot from heat. Cover the Dutch oven with a lid (the lid needs to fit very snugly; if it doesn't, first tightly cover the pot with a piece of foil).

Bake the brisket on middle rack of oven until tender when pierced with a fork, about 4 hours.

Check to see that brisket is done. Remove from oven or add time as needed.

Transfer the meat to a cutting board and tent loosely with foil.

Strain the liquid from the Dutch oven through a colander into a large bowl. Set the vegetables aside. Measure the liquid; you should have about 2 cups. Add beef broth if needed (or if you have too much liquid, save it for another use).

Pour 1/4 cup of the strained liquid into a medium saucepan. Add the cornstarch and whisk until the mixture is completely smooth. Stream the remaining liquid into the saucepan and whisk to combine. Set over medium heat and cook, whisking steadily, until sauce bubbles and thickens, 2-4 minutes. Transfer to a gravy boat or serving bowl.

Cut the brisket into wide slices and transfer to a serving platter. Discard the herb stems and bay leaf from the carrots and onions, then spoon vegetables around the meat. Scatter the fresh thyme leaves over the meat and carrots and tuck in thyme sprigs. Serve with the gravy.