1. Combine beef and next 4 ingredients in a medium bowl; shape into 4 thin patties.
2. Cut Brie into small pieces, and place half of the pieces in the center of each of 2 of the patties; top with remaining patties, pressing to seal edges.
3. Heat oil in a large skillet over medium-high heat; add burgers, and cook, 2 to 3 minutes on each side or to desired degree of doneness. Serve on buns with toppings.