Sauté the onions in oil over medium-high heat until translucent. Remove from heat and allow to cool.
Mix all of the ingredients together (including the onions). Do not overwork the meat.
Form patties of about 1/4 to 1/3 lb (115 to 150 g) each.
Cook in oil over medium heat for about 6 to 7 minutes per side, until an internal temperature of 140°F (60°C) for medium and 160°F (71°C) for well done. (Do not press down on the patties during cooking and avoid flipping too often; this will dry out the burgers.)
In the meantime, fry mushrooms in a pan for 5 to 10 minutes until golden.
Let burgers rest for 5 minutes. Serve with lettuce, tomatoes, mushrooms and brie cheese.
