Tomato: Whisk the balsamic vinegar, oil, salt and pepper in a small bowl. Pour over tomato slices to marinate.
Burger: Preheat a barbecue for medium-high heat and lightly oil the grate.
Mix mince, tomato paste, basil, Parmesan cheese, garlic and pepper in a large bowl. Form beef mixture into 4 equal patties.
Cook on the barbecue until the burgers are cooked; about 5 minutes per side for well done. Top each burger with mozzarella cheese and allow to melt. Serve on hamburger buns with marinated tomato slices.