In a bowl, mix all together the ingredients for the burger patties. Set aside at cool for 20 to 30 minutes.
Meanwhile, prepare the garnishing. Mince the onion or the sliced leeks and the mushrooms. Slice the cheese into 8 slices and set aside at cool.
In a pan, heat oil at medium heat. Cook onion or sliced leeks and the mushrooms for 2 to 3 minutes, until they brown. Add garlic and parsley and season. Remove from fire. Cover and set aside.
Make 4 patties with a thickness of about 2 cm (3/4 inch). In a pan, heat the oil at medium heat. Cook the patties for 5 minutes on each side or until the inside is no longer pink.
Meanwhile, Preheat the oven to broil. Open the bread buns and broil in the oven for about 1 minute.
Garnish the bread buns with patties, slices of brie and the sauté mushrooms.