- Preheat the grill, setting the burners on high. Oil the grate.
- Oil the bell peppers and zucchini. Season with salt and pepper. Place the peppers on the grill, skin side down. Brush with oil and cook for 8 to 10 minutes or until the skin is well charred. Place the peppers in an airtight container. Let cool. Remove the skin. Set aside.
- Grill the zucchini on each side. Set aside.
- In a bowl, combine all of the ingredients. Season with salt and pepper. With your hands or with a hamburger press, shape the meat mixture into four patties.
- Grill the patties for 4 to 5 minutes on each side or until cooked through. Season with salt and pepper.
- Toast the buns. Spread the inside with mayonnaise and mustard. Place the patties on the bun bottoms. Layer with the cheese, zucchini, tomato, bell pepper and basil. Cover with the bun tops.
Most supermarkets will carry balls of bocconcini or Mozzarina, which is very similar to mozzarella di bufala. It is often more expensive than bocconcini, but creamier and very tasty.