Heat an outdoor grill for high heat. Remove the steak from refrigerator and let stand at room temperature while you prepare the tomatoes.
To prepare the tomatoes: in a medium bowl, mix the parmesan cheese, panko and basil. Place the tomatoes on a small rimmed baking sheet and coat them all over with 1 tablespoon olive oil. Turn the tomatoes cut-side-up and then season them all over with salt and pepper, and pat a generous topping of the parmesan mixture on the top of each one. Drizzle with the remaining 1 tablespoon of olive oil.
Turn off one burner if using a gas grill, or keep the coals on one side of a char grill to create areas of both direct and indirect heat. Put the baking sheet of tomatoes on the cooler area of the grill. Cook with the lid closed for 5 minutes.
Meanwhile, to prepare the broccolini and steak: In a large bowl, toss the broccolini with the olive oil, garlic, lemon zest and red pepper flakes to coat. Season with salt and pepper. Coat the steak with a tablespoon of olive oil and season with salt and pepper.
After the tomatoes have cooked for 5 minutes, place the steak and broccolini on the grill over the lighted burners or coals. Cook, with the lid closed, turning the broccolini occasionally and turning the steak through cooking, for a total of 6 minutes, or until the meat feels only slightly resilient when pressed with a fingertip and instant-read thermometer inserted into the center of the steak registers 120F for medium-rare. Transfer the steak to a platter and let rest for 5 minutes. Meanwhile, continue cooking until the broccolini is tender and begins to char and the topping of the tomato is golden brown, about 2 minutes more. Add the broccolini and tomatoes to the platter.
Transfer the steak to a cutting board and cut it across the grain into 1/4-inch thick slices. Divide the sliced steak, tomatoes and broccolini among four dinner plates. Drizzle with balsamic vinegar; sprinkle with salt and serve.