1. Trim excess fat from the brisket, but leave a thin layer of it intact. Season it all over with salt, rubbing it into the meat. Put the brisket in a shallow baking dish, cover, and refrigerate overnight.
2. Sprinkle the brisket with the flour. Heat the oil in a large, wide pot or roasting pan over medium-high heat on the stovetop and brown the brisket on both sides, which will take about 10 to 15 minutes, total. Transfer the brisket back to the baking dish.
3. Preheat the oven to 350ºF (180ºC).
4. Lower the heat to medium and add the sliced onions to the pot, season them with a bit of salt and black pepper, and cook, stirring frequently, until they are soft, wilted, and golden brown. While cooking them, scrape up any stuck on bits of beef from the bottom of the pan, and stir them into the onions. If the pan is too dry and the onions are sticking to the bottom, add a tablespoon or so of water. The onions will take about 10 to 15 minutes to cook.
5. Add the brisket back to the pot, laying it over the onions, along with any juice that may have pooled in the dish it was resting in. Smear the tomato paste over the brisket, sprinkle with the fish sauce (if using), the garlic slices, and the diced carrots. Cover and cook in the oven for 1 1/2 hours, lifting the lid once or twice during cooking, to spoon any juices over the brisket.
6. Remove the pot from the oven and reduce the heat of the oven to 325ºF (160C). Set the brisket on a cutting board and slice it in 1/2-inch (1,25) slices against the grain, or thinner if you like, then place the slices back in the pot so that they are snugly overlapping, keeping them in the same order as they were when you sliced them. Cover the pot and bake for another 2 hours, or until tender.
You can serve the brisket right away, or let it cool and refrigerate it overnight. (It’s actually better served 2-3 days after it’s baked.) The beef slices can be rewarmed in the pot along with the sauce.