Preheat the oven to 325 degrees F.
In a large enameled cast iron casserole, heat 2 tablespoons of the olive oil. Season the brisket with salt and pepper. Add half of the brisket to the casserole and cook over medium-high heat, turning on all sides until browned, about 6 minutes. Transfer the brisket to a plate. Repeat with the remaining oil and remaining brisket. Add the celery, carrot, onion, and chile to the casserole and cook over medium heat until softened, about 7 minutes. Add the tomato paste and cook, stirring frequently, until glossy, about 2 minutes. Add the thyme sprigs, anchovies, bay leaf, and garlic and cook for 2 minutes, stirring frequently. Add the stock, wine, and vinegar and bring to a boil. Return the brisket to the casserole, cover and braise for 1 hour. Drop the heat to 225 degrees F and cook 4 more hours or until meat is tender.
If you are concerned if the oils or other ingredients in these recipes are suitable for Passover, seek non-dairy substitutes or ingredients that are certified kosher for Passover.