Heat a drizzle of olive oil in a frying pan until shimmering, then add the mushrooms and a few splashes of Worcestershire sauce. Season well, then fry over a high heat until the mushrooms are browned. Drain on kitchen paper, then set aside to cool completely. When cool, put them in a food processor and beat until you have a very fine mushroom paste.
Meanwhile, heat another drizzle of oil in the frying pan. Fry the onion, stirring, over a medium-high heat for 10 minutes or until brown and soft, adding a splash of water now and then to prevent it burning. Set aside.
Add the beef mince to the mushroom paste and season. Mix, then form into burgers.
Heat the frying pan over a high heat, uncovered, until hot. Brush the burgers all over with oil, then add to the pan and cook for 3 minutes. Flip and cook on the other side for 1 minute, then top with the onions and cheese. Add 2 tbsp water to the pan, then cover and cook for 1 ½ minutes or until the burgers are cooked and the cheese is melted. Put the burgers on a plate, cover loosely with foil and rest for 2 minutes.
Meanwhile, toast the cut side of the bun halves in the pan on a medium- high heat, so they soak up the burger juices (if the pan is very wet, first increase the heat, so most of the liquid is bubbled away and then add the bun). Put the burgers in the buns with a lettuce leaf and some mustard and ketchup. Secure with a wooden skewer, then serve with pickles on the side, if you like.