Thinly slice half an onion. Saute onion in a pan with olive oil until golden brown and caramelized. Remove onion from pan, setting aside of later. In the same pan, saute mushrooms.
In a small bowl, mix together your favourite BBQ sauce with a splash of bourbon or whisky for added flavour (optional). Add dijon mustard.
In a large bowl, mix together ground beef, egg, Worcestershire sauce and salt and pepper (to taste). Form mixture into four large patties. Patties should be larger than bun, as they'll shrink when grilled. Grill burgers on the BBQ over medium-high heat until cooked as desired.
Slice onion buns in half, and top with lettuce, burger, sauce, cheese, caramelized onions and mushrooms.