Prepare the beef and sear it deeply. Pat the beef dry with kitchen paper, then season generously all over with salt and pepper. Heat the olive oil in a large, heavy-based pot or Dutch oven over a high flame until it shimmers and you see the first wisp of smoke. Lower the beef in carefully — you should hear a fierce, satisfying sizzle. Sear for 4–5 minutes per side, until each face is a deep, mahogany brown. The crust should feel firm and smell intensely savoury. Remove the beef to a plate.

Soften the onions and garlic. Reduce the heat to medium. Add the sliced onions to the pot; they will hiss and release a little moisture. Stir them, scraping up the browned bits from the bottom. Cook for 10–12 minutes, until they turn translucent and golden at the edges, and the kitchen fills with a sweet, mellow aroma. Add the smashed garlic and cook for one more minute, until fragrant.

Build the braising liquid. Stir in the tomato purée and cook for 2 minutes, stirring constantly, until it darkens and smells richer. Pour in about 250 ml of the hot stock and scrape the pot bottom thoroughly to lift every last caramelised speck. Then add the remaining stock, the rosemary, thyme, bay leaves, peppercorns, and Worcestershire sauce. Bring to a gentle simmer — you should see small, lazy bubbles, not a rolling boil.

Braise low and slow. Return the beef to the pot, along with any juices from the plate. The liquid should come about halfway up the meat. Cover with a lid and place in the oven at 160°C (fan-assisted). Let it cook for 2 hours 30 minutes to 3 hours. At the 2-hour mark, check the texture: a fork should slide into the beef with moderate resistance. The liquid should be deeply fragrant, with a colour like dark caramel.

Rest the beef. Remove the pot from the oven and lift the beef onto a cutting board. Tent it loosely with foil and let it rest for at least 20 minutes. During this time, the fibres relax and reabsorb their juices, ensuring every slice stays succulent. Do not skip this step — it makes the difference between moist slices and dry ones.

Strain and season the au jus. While the beef rests, strain the braising liquid through a fine-mesh sieve into a clean saucepan, pressing on the onions and herbs to extract all the flavour. Discard the solids. Skim off any excess fat from the surface. Taste the jus and adjust salt and pepper — it should be intensely beefy and savoury. Keep it warm over a low flame.

Slice, assemble, and serve. Slice the beef thinly against the grain — aim for slices about 5 mm thick. They should glisten and hold together. Split the rolls and lightly toast them. Pile the beef onto the bottom halves, add a slice of cheese if using, and spoon a little warm jus over the top to soften the bread. Place the top halves on, and serve immediately with small bowls of the remaining au jus for dipping.