Preheat an outdoor grill for high heat and lightly oil grate.
Whisk egg, salt, and pepper together in a medium bowl.
Add ground beef and bread crumbs; mix with your hands or a fork until well blended.
Form into four ¾-inch-thick patties.
Place patties on the preheated grill. Cover and cook 6 to 8 minutes per side, or to desired doneness. An instant-read thermometer inserted into the center should read at least 70°C.