In a small bowl, whisk balsamic vinegar, olive oil, salt, and ground black pepper.
Place tomato slices in the bowl to marinate.
Preheat the outdoor grill to medium-high heat and lightly oil the grate.
In a large bowl, mix ground beef, tomato paste, basil, Parmesan cheese, garlic, and ¼ teaspoon ground black pepper.
Form the beef mixture into 4 equal patties.
Place the patties on the preheated grill.
Cook each side for about 5 minutes or until they reach your desired doneness. Use an instant-read thermometer to ensure the internal temperature is 160°F.
Top each burger with mozzarella cheese and let it melt.
Place each burger on a hamburger bun.
Add marinated tomato slices to the burgers and serve.