Preheat the oven to 160C/140C Fan/Gas 3.
To make the brisket, season the beef all over with salt and pepper. Heat 2 tablespoons of the oil in a large flameproof casserole and brown the beef over a high heat for 8–10 minutes, turning every couple of minutes. Remove the beef from the casserole and set aside.
Add the sliced onions to the casserole and fry for 5 minutes or until nicely browned. Stir in the thyme and bay leaf and cook. Return the beef to the casserole. Stir the tomato purée into the hot beef stock and pour around the beef. Add the wine and bring to a gentle simmer on the hob. Cover with a lid cook in the oven for 3 hours, turning after about 1½ hours.
Heat another tablespoon of oil in a large non-stick frying pan on a medium heat. Fry the quartered onions for 5 minutes, stirring occasionally. Add the carrots and celery and cook for a further 5 minutes, until the onions are softened and all the vegetables are lightly browned.
Remove the beef from the oven and nestle the vegetables around it. Cover and return to the oven for a further 1–2 hours.
To make the potato latkes, whisk the egg and egg yolk together in a small bowl. Place the onion and potato in a large colander, mix well and squeeze out as much liquid as possible over a sink. Place the squeezed vegetables in a clean bowl and add the beaten eggs, flour, salt and parsley or chives (if using) to the onion and potatoes. Season with lots of pepper and mix well.
Pour 2 tablespoons of the oil into a large non-stick frying pan and place over a low-medium heat. Take a handful of the potato mixture and form into a loose ball. Place in the pan and flatten with a spatula until around 1.5cm/½in thick. Repeat with 3 more balls of the potato until you have 4 latkes cooking at the same time.
Cook the latkes for 6–8 minutes on each side until golden-brown and cooked through. Don’t be tempted to increase the heat or the latkes will burn on the outside before they are ready in the middle. Put on a baking tray and set aside while you cook the remaining latkes. Add an extra 2 tablespoons of sunflower oil to the pan between batches.
Turn the oven up to 200C/180C Fan/Gas 6. When you are almost ready to serve the latkes, reheat on the baking tray in the oven for 10–15 minutes, or until hot and crisp.
Lift the beef out of the casserole with a couple of forks and place on a board or serving platter. Cut off the string and carve into slices. Serve with the poached vegetables, latkes and the rich cooking liquor for gravy.