You MUST chop the onions and parsley by hand. If you put them in a food processor their juices will drain and burn during the cooking process.
Mix the ground beef, onions, and parsley in a large flat baking pan. The best way to do this is to spread the beef thin and then add the chopped parsley and onions on top. Mix the ingredients back into a ball and then spread the meat out thin again in the pan to increase it's surface area. Then, season the meat while it's spread thin on the pan with salt and pepper, generously, then reform the meat into a ball again. Go through this at least twice to make sure the mixture is well seasoned.
Divide the seasoned ground beef into 4 equal portions and form them into 4 patties (you can also choose to make them smaller, but the cooking time with change).
Cook the burgers on a searing skillet (or grill) for about 4-5 minutes on each side for a medium-cooked burger.
Lightly grill a piece of brie on the grill or skillet (it will melt quickly). Add the swiss cheese and the grilled brie on top of the burger, then serve on a bed of arugula on toast.