Preheat oven to 375 degrees. Lightly grease a large Dutch oven or roasting pan with a lid.

Dust the brisket with flour and season generously with salt and pepper. Heat the oil in the Dutch oven over medium-high heat. Add the brisket and cook until brown and crusty, about 6 minutes per side.

Transfer the brisket to a large platter or baking sheet; set aside. Add the onions to the Dutch oven and cook until soft, about 10 minutes.

Remove the pot from the heat and place the brisket over the onions, along with any juices that have accumulated on the platter. Spread the tomato paste evenly over the brisket.

Add the garlic and carrots to the pot. Cover and cook for 1 1/2 hours.

Transfer the brisket to a cutting board. Using a sharp knife, thinly slice the brisket across the grain. Return the slices to the pot overlapping each other, along with any juices from the cutting board. Add a tablespoon of water to the pot.

Lower the oven to 325 degrees. Return the brisket to the oven, covered, and cook until fork tender, 3-4 more hours. Check once or twice during cooking and add more liquid if needed, a tablespoon at a time. Each time you check, spoon some pan juices over the brisket.

You can serve the brisket immediately, or cover it loosely with foil and refrigerate overnight. To reheat, skim and fat from the surface and reheat in a covered Dutch oven for about one hour, until just warmed through.