Put the beef, onion, garlic, thyme and some salt and pepper in a bowl. Using your hands, work them together until evenly combined and slightly sticky. Divide the mixture into quarters and shape into 4 even-sized patties. Chill for 30 minutes.
Brush the patties with a little oil and cook on a hot barbecue for 5–6 minutes on each side until cooked through and lightly charred on the outside. Top the burgers with cheese and place under a hot grill for 30 seconds until melted.
Meanwhile, toast the buns on the barbecue for 1 minute on the cut side.
Fill each bun with the lettuce leaves, cheese-topped patties and tomato slices.