Mix tuna, mushroom soup, milk, eggs, salt, and black pepper in a large mixing bowl. Stir stuffing mix into tuna mixture until thoroughly combined. Form mixture into patties. Refrigerate patties for 10 minutes to firm up.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Grill patties until heated through and the outsides show grill marks, about 7 minutes per side.