1. Heat half the oil in a frying pan and cook the onion over a low-medium heat for 15–20 minutes, stirring occasionally, until soft and golden. Add a spoonful of water if it catches.
2. Mix the mayonnaise with the black truffle sauce. Shape the beef into two loose patties, slightly wider than the buns, and season both sides just before cooking.
3. Heat the remaining oil in a heavy frying pan over a medium-high heat. Cook the patties until browned and cooked to your liking; for minced beef, the safest choice is to cook thoroughly. Add the Cheddar during the final minute and cover briefly to melt it.
4. Toast the cut sides of the buns. Spread both halves with truffle mayo, then add lettuce, a burger and the onions. Serve immediately.