Prepare the beef: Pat the sliced beef dry with kitchen paper. Season generously with salt and pepper on both sides. The meat should look dry and slightly tacky to the touch, which helps it brown beautifully rather than steam.

Sear the meat: Heat the olive oil in a large frying pan over high heat until it shimmers and a drop of water sizzles instantly. Add the beef slices in a single layer — you may need to do this in two batches. Cook for 1-2 minutes per side until the edges are deep brown and the kitchen smells wonderfully savoury. Transfer the seared beef to a plate; it should look caramelised and fragrant.

Cook the onions: Reduce the heat to medium. Add the sliced onions to the same pan. Stir with a wooden spoon, scraping up any browned bits from the bottom — this adds incredible depth. Cook for 5-6 minutes until the onions are soft, translucent, and just starting to turn golden at the edges.

Build the au jus: Add the minced garlic and cook for 30 seconds until fragrant, then pour in the beef stock, Worcestershire sauce, soy sauce, dried thyme, and bay leaf. Stir well, scraping the pan bottom again. Bring to a gentle simmer — you’ll see small bubbles rising steadily to the surface, but not a vigorous boil.

Simmer the beef: Return the seared beef slices to the pan along with any juices that have collected on the plate. Reduce the heat to low and let everything simmer gently for 8-10 minutes. The liquid should reduce slightly and thicken just enough to coat the back of a spoon. The beef will become tender and the onions will soften further, creating a rich, savoury broth.

Toast the rolls: While the beef simmers, split the bread rolls in half and spread the cut sides with softened butter. Place them under a hot grill for 2-3 minutes until golden brown and crisp around the edges. Keep an eye on them — they go from perfect to burnt very quickly.

Assemble the sandwiches: Remove the bay leaf from the pan. Use tongs to pile the beef and onions onto the bottom halves of the toasted rolls. Top each with a slice of cheese. Place the assembled sandwiches back under the grill for 1-2 minutes until the cheese melts and becomes bubbly and slightly golden. Place the top halves of the rolls on.

Serve with au jus: Ladle the remaining hot broth from the pan into small bowls for dipping. Serve the sandwiches immediately, with the au jus on the side. The rolls should be crisp on the outside, soft inside, and the beef should be tender enough to pull apart with your fingers.