Mix the meat, egg, salt and pepper in a large bowl. Lightly form 8 even hamburger patties. Set aside.
In a smaller bowl, mix blue cheese and chopped walnuts until combined.
Evenly divide the blue cheese and walnut mixture onto 4 of the hamburger patties. Top with the remaining 4 beef patties, pinching the edges together to seal the cheese completely. Make sure the cheese is well stuffed into the burger so it doesn’t burst out of the sides during the cooking process.
Cook the hamburgers for about 4 minutes on one side. Turn them over and cook another 2-3 minutes on the other side for medium-rare. Burger can be cooked on a grill or in a pan on the stove top. Remove the burgers once done cooking and allow to rest for 5 minutes.
Serve with lettuce, tomato and red onion on a bun.