Caramelize the onions: Heat the olive oil and butter in a large frying pan over a medium heat. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, for 15-18 minutes. You'll notice the onions soften and turn a deep golden brown, releasing a sweet, rich aroma. The sizzle will quieten as they release their moisture.

Finish the onions: Sprinkle the brown sugar over the softened onions and stir. Add the balsamic vinegar and cook for another 2 minutes. The vinegar will hiss as it hits the pan, then mellow into a glossy, sticky coating. Scrape the onions into a bowl and set aside. Wipe the pan clean with a paper towel.

Form the patties: In a large bowl, combine the beef mince with the salt, pepper, garlic powder, and onion powder. Use your hands to gently mix, being careful not to overwork the meat. Divide the mixture into four equal portions and shape them into patties about 2cm thick. Use your thumb to press a small indent into the centre of each patty — this prevents them from puffing up into balls as they cook.

Cook the burgers: Return the same frying pan to a high heat. Place the patties in the hot, dry pan. You should hear a loud sizzle immediately — that's the sound of a good sear. Cook for 4-5 minutes on the first side. The edges will turn brown and a crust will form on the bottom. Flip the patties using a spatula. If using cheese, place a slice on each patty now and cover the pan with a lid for the final minute. Cook for another 3-4 minutes for medium. The cheese will melt into a gooey blanket, and the burger will feel firm but give slightly when pressed.

Toast the buns: While the burgers rest, place the split buns cut-side down in the pan for about 30 seconds. They should turn golden and crisp, with a light toast smell.

Assemble the burgers: Place a lettuce leaf and a tomato slice on the bottom half of each bun. Top with a burger patty and a generous spoonful of caramelized onions. Close with the top bun and serve immediately.