Finely chop the shallot.
In a large bowl mix the mince, egg yolk, mustard, garlic, thyme leaves and Parmesan. Season with salt and pepper.
Form 4 patties and put them on a plate. Cover and keep in the fridge until cooking.
Heat the BBQ, grill or griddle pan to medium-high. Cook the patties for 5 minutes on each side. If you want cheese burger - put a slice of cheese on the patties when turned over and cover them with a lid or metal container to help the cheese melt.
Meanwhile cut the buns in half and toast them - preferably just the cut side. Top the bottom halves with lettuce, tomato & onion slices, pickled cucumber, Parma ham etc - then add the patties. Spread some ketchup, mustard or mayo on the top bun halves, and place these on top of the patties.
Serve warm.