Boil the balsamic vinegar and sugar in a heavy small saucepan over medium-high heat until reduced to 1/3 cup, stirring occasionally, about 18 minutes.

Meanwhile, preheat the broiler. Melt the butter in a heavy large skillet over medium-high heat. Sprinkle the steaks with salt and pepper. Cook the steaks to desired doneness, about 3 minutes per side for medium-rare. Transfer the steaks to a baking sheet. Crumble the cheese over the steaks and broil just until the cheese melts, about 1 minute. Sprinkle with pepper.

Transfer the steaks to plates. Drizzle the balsamic sauce around the steaks and serve.