Preheat a grill to medium high. Put the flank steak between 2 sheets of plastic wrap and pound with a meat mallet until the thickest part is 3/4 inch thick. Season with salt and pepper and rub with 1 tablespoon olive oil, the rosemary and garlic. Let sit 10 minutes before grilling.
Meanwhile, slice the larger tomatoes into wedges and halve the smaller tomatoes. Place in a medium bowl and add the vinegar and 2 tablespoons olive oil. Season with salt and pepper and toss.
Oil the grill grates. Grill the steak until well marked, about 4 minutes per side for medium rare. Transfer to a cutting board and let rest 5 minutes.
Spoon the tomatoes and their juices onto plates and add the mozzarella. Slice the steak against the grain and add to the plates. Drizzle with the remaining 1 tablespoon olive oil, season with pepper and top with basil.