A good way to tell if these burgers are cooked to your liking—without cutting into them to peek—is to watch how the meat cooks on the sides. When the raw pink color first disappears you know they’re still rare in the middle; a couple of minutes after that they should reach medium rare.Serves four.
Gently break the meat into large pieces in a large bowl. Add the Worcestershire sauce, 1 tsp. salt, and 1/2 tsp. pepper and gently mix with your hands; avoid overworking.
Wet your hands and shape the meat into 8 equal 1/2-inch-thick patties. Make a slight indentation in the center of 4 of the patties to hold the cheese. Divide the blue cheese into 4 equal portions, shape into disks, and set a disk in each of the 4 indentations. Top the cheese with the remaining patties and gently but firmly seal the edges to completely encase the cheese. Refrigerate, uncovered, for at least 20 minutes and up to 4 hours.
Prepare a hot charcoal or gas grill fire. Grill the burgers, covered with vents open, until nicely marked and cooked to your liking (2 minutes per side for rare, 3 minutes per side for medium rare, 4 minutes per side for medium). Don't press on the burgers while they're cooking—you want to keep the juices and cheese inside the burger, not on your grill.
Serve with the Red Wine Pan Sauce.