Combine all the sauce ingredients in a small bowl.
Toss the lettuce and ¼ cup of the sauce together in a medium bowl. Set aside the remaining sauce for serving.
Preheat the griddle over high heat for 10 minutes.
Form the ground beef into 8 equally sized balls (4 oz. each).
Toast the buns until lightly browned, 1–2 minutes. Place on a tray and spread some of the remaining sauce on each side of the bun. Keep the prepared buns, cheese, and lettuce close by the griddle.
Place the meatballs onto the griddle, leaving space between each ball for the burger to spread. Use a burger press or the back side of a wide spatula to smash the burger into a thin patty (parchment paper between the press and the burger will help keep the burger from sticking).
Season the burgers with the salt and pepper and cook, undisturbed until the edges of the burger are brown and only slightly red in the center, 3–4 minutes.
Flip the burgers and top with the cheese. Allow the cheese to melt, about 1 minute.
Place two burger patties on each bun and top with the lettuce to serve.
