Prepare the patties: In a large mixing bowl, gently combine the beef mince with the salt and pepper. Use your fingertips to mix lightly—overworking the meat will make it tough. Divide the mixture into four equal portions (about 125g each). Roll each portion into a ball, then flatten into a patty roughly 2cm thick. Press your thumb into the centre of each patty to create a shallow dimple; this stops them from puffing up into a dome as they cook. You should see a uniform, round shape with a small indent in the middle.

Make the sauce: In a small bowl, stir together the mayonnaise, Dijon mustard, tomato ketchup, and the minced garlic. The sauce should be a pale, creamy pink colour with a smooth, spoonable consistency. Set it aside.

Toast the buns: Spread the softened butter onto the cut sides of the brioche buns. Place a large frying pan over medium heat. Once the pan is hot, place the buns buttered-side down in the pan. Toast them for 60-90 seconds, until they turn a deep, golden brown and smell wonderfully nutty. The edges should feel crisp to the touch. Remove them and set aside.

Cook the patties: Increase the heat under the pan to medium-high and add the vegetable oil. When the oil shimmers and a light haze forms, carefully place the patties dimple-side up into the pan. You should hear a satisfying sizzle immediately. Cook for 3-4 minutes without moving them. The bottom will develop a dark, caramelised crust, and the edges will begin to turn a light brown. The raw top will start to look opaque near the edges.

Flip and add cheese: Using the fish slice, flip each patty carefully. The cooked side should be a rich, deep brown with a crisp texture. Place a slice of cheese on top of each patty. Cook for another 3-4 minutes for a medium doneness. The cheese will begin to melt and droop over the sides. The centre of the patty should feel slightly firm when pressed gently with the back of the spatula.

Rest the patties: Once cooked, transfer the patties to a clean plate and allow them to rest for 2 minutes. This crucial step lets the juices redistribute throughout the meat, ensuring every bite is moist. You'll notice a small pool of juices forming on the plate—this is flavour you've saved.

Assemble the burgers: Spread a generous layer of the sauce on the bottom half of each toasted bun. Place a lettuce leaf on the sauce, followed by the cheesy patty. Top with two tomato slices and a few rings of red onion. Add a couple of pickled cucumber slices if you like. Finish with the top half of the bun, pressing down very gently to secure everything.

Plate and serve: Place each burger on a plate with the cut side facing you, showcasing the beautiful layers. For a polished presentation, skewer the burger with a long cocktail stick to hold it together. Serve immediately while the cheese is still molten and the bun is warm.