Place the ground beef, breadcrumbs, egg, Italian seasoning, garlic, parsley, salt, and pepper in a large bowl. Mix with your hands until the ingredients are evenly combined but not overworked.
Divide the mixture into four equal portions and shape each into an oval steak about 1 inch thick.
Preheat a grill to medium heat and lightly oil the grates. Place the steaks on the grill and cook for 5 to 6 minutes per side until they reach an internal temperature of 160 degrees.
Lay one slice of mozzarella on each steak during the last minute of cooking so it melts.
While the steaks finish, combine the cherry tomatoes, basil, olive oil, and balsamic vinegar in a small bowl and toss gently.
Remove the steaks from the grill and spoon the tomato basil mixture over the melted mozzarella before serving.