Heat oil in a heavy saucepan over medium heat and saute bacon until just cooked but not crisp.
Add shallots and cook until translucent. Add mushrooms and continue cooking until water evaporates, about 5 minutes.
Transfer mixture to a large mixing bowl and let cool. Add salt, pepper, Worcestershire sauce and egg to mixture. Add beef and gently mix by hand until all ingredients are incorporated, without over-mixing.
Divide mixture into 16 equal portions. Form into thick patties, about 1-1/2 inches thick and 2-1/2 inches in diameter, tucking a piece of cheese and 2 walnut halves into the centre of each patty.
Grill patties on medium-high heat until cooked to preferred doneness. Serve in small dinner rolls or between baguette slices with desired condiments.