Preheat the oven to 350 F while you peel and slice vegetables.
Pat your brisket dry and place it fat side up on top of the sliced onions. Add the carrots around the brisket along with the rosemary sprigs and garlic cloves.
Season the brisket additionally if you wish – do not add salt. Sprinkle the thyme leaves on top of the brisket.
Put in the oven, uncovered, for 1 hour so that the beef browns and the fat begins to render.
Turn the oven down to 325 F; pour the tomato sauce over the top of the beef, then cover and return to the oven for 4 hours.
If the fat has rendered completely, flip the brisket and return to the oven, covered, with the temperature reduced to 250 F for a final hour to finish.
To serve same-day: rest brisket for 30 minutes while you skim the fat from the pan juices (remove the vegetables first and reserve them for plating later). Slice and serve with the Au Jus (no need to reduce) and reserved vegetables.
To serve the next day: refrigerate once brisket is rested, leave whole. Remove vegetables from the pan juices. Place the pan juices in a separate container and also refrigerate. Once the fat has risen to the top and solidified the next day, remove in one piece and set the Au Jus aside. Slice as much brisket as required and place in an oven proof dish. Add enough beef stock to the dish to cover the bottom, then wrap in foil and place in a 300 F oven for 30 – 45 minutes to reheat. Heat the Au Jus on the stovetop and serve alongside the brisket.