Combine the beef and sausage in a large bowl and mix well.
Gently shape the meat mixture into 4 or 5 patties. Make the patties slightly larger than the size of your bun as they will shrink slightly as they cook. Season all over with salt and pepper.
Heat a griddle to medium-high.
Cook the patties, flipping once, until almost cooked through, about 5 minutes on the first side and 3 minutes on the second side.
Divide the cheese evenly among the burgers and cook until melted and the burgers have reached an internal temperature of 160°F (71°C), about 2 minutes more.
Serve on burger buns, offering lettuce, tomato, and onion on the side, if desired.
Notes
Shape gently--Use a gentle hand when shaping your burgers. You want to pack the meat tightly enough to hold together, but not so tight that the burger is tough. I find it easiest to cup my hands around the beef when shaping, and gently pat them into an even round.
Dietary--This recipe is suitable for gluten-free diets, if served on a gluten-free bun.