Start the onions. Place a large frying pan over a medium-low heat and add the butter and olive oil. Once the butter has melted and is gently foaming, tip in all the sliced onions. Stir them well to coat in the fat, then spread them out in an even layer. Let them cook undisturbed for 10 minutes; you will hear a gentle, steady sizzle. After 10 minutes, stir, and you will see the onions have softened and become translucent. Sprinkle over the salt and sugar, stir again, and reduce the heat to low. Cook for a further 25-30 minutes, stirring every 5 minutes, until the onions are a deep, sticky, mahogany brown. They should feel silky and smell intensely sweet and savoury. Deglaze the pan with the beef stock, scraping up any brown bits from the bottom, and let it cook for 2 minutes until the liquid has evaporated.

Prepare the patties. While the onions cook, place the beef mince in a mixing bowl. Add the smoked paprika, garlic powder, and black pepper. Using your hands, gently mix the seasonings into the mince — do not overwork the meat, as this will make the burgers tough. Divide the mixture into 4 equal portions and shape them into patties, about 2.5cm thick. Make a small, shallow indent in the centre of each patty with your thumb; this helps them cook flat rather than puffing up into a ball.

Cook the patties. Heat a separate large frying pan or griddle over a high heat until it is smoking hot. Carefully lay the patties into the dry pan — you should hear a loud, satisfying sizzle on contact. Do not move them. Cook for 4 minutes on the first side. You will see the edges turning brown and the juices beginning to rise to the surface. Flip the patties using a spatula. If you are adding cheese, lay a slice on top of each patty now. Cook for another 3-4 minutes for medium, or longer if you prefer well-done. The cheese will melt into a luscious blanket over the meat.

Toast the buns. While the patties rest, split the burger buns in half and place them cut-side down in the same pan (with the heat turned off). Let them sit for 30-60 seconds until they are lightly golden and fragrant. This step is crucial for texture — it prevents the buns from going soggy.

Assemble the burgers. Place the bottom half of each bun on a plate. Add a layer of lettuce and a slice of tomato. Place the cheese-topped patty on top. Spoon a generous heap of the caramelized onions onto the patty. Add pickles if you like, then crown with the top bun. Press down gently and serve immediately.