Instead of turning ground beef into a patty, chef Tim Love shapes the meat into loaves that resemble hot dogs, called Burger Dogs.
Make the Wild Game Rub: Combine all ingredients and mix well. Store what you don't use in a separate container and keep it in a dry cool place, like your pantry.
Heat the grill to high.
In a food processor, combine the sirloin and brisket and pulse until ground.
Transfer the meat into a large bowl. Add the mayo, shallot and Wild Game Rub, then gently mix. Divide the meat into four equal portions. Make each portion of the meat into the shape of a hot dog to create a Burger Dog.
Place the Burger Dogs on the hot grill and shut the lid. Cook for 4 minutes, then lift the lid, flip the Burger Dogs and close the lid again. Lightly toast the hot dog buns and then set aside.
Sear each Burger Dog on all four of its sides, about 2½ minutes per side for medium. During the final minute of grilling, top each Burger Dog with a slice of cheese. Once the temperature reaches 140°, remove the Burger Dogs from the grill and place them into the grilled buns. Serve with lettuce, tomato, onion and relish.