Preheat grill so that the grill is very hot or preheat a large skillet on the stovetop on medium-high. mix shallots and blue cheese. Divide ground beef into 4 equal parts and flatten into large patties. Spread 1/2 of the mixture onto one patty, leaving a 1/4 inch border around the edges. Press another patty on top and press around the edges to seal, forming one patty. Repeat. Cook on hot grill until burgers reach desired doneness.