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In a large pot of salted boiling water, boil potatoes until tender, 12 minutes. Drain and halve if large. Heat broiler. Transfer potatoes to a large rimmed baking sheet and toss with 2 tablespoons olive oil, garlic, and chopped rosemary. Season with salt and pepper. On a plate, rub steak with remaining tablespoon oil and balsamic vinegar and season generously with salt and pepper. Nestle in the middle of the potatoes and scatter rosemary sprigs on pan. Broil until steak is medium, 4 minutes per side. Let rest, then slice and serve.