Pat steak dry; salt and pepper both sides of steak. Heat 1 Tbsp. EVOO in a heavy skillet over moderately high heat until hot but not smoking, then cook meat for five minutes each side for medium rare (depending on thickness of steak).
Transfer steak to a cutting board and let rest for 10 minutes. Holding knife at a 45° angle, cut steak across the grain into thin slices. Transfer to plate and drizzle with balsamic vinegar and EVOO.