Combine scallions and next 7 ingredients in a large resealable plastic bag and mix well. Add steak; seal bag, pressing out excess air. Turn steak to coat. Refrigerate overnight, turning bag occasionally.
Build a medium-hot fire in a charcoal grill, or heat a gas grill to high. Remove steak from bag; wipe off excess marinade. Season both sides lightly with salt. Grill steak until well browned, about 6 minutes per side for medium-rare. Transfer to a cutting board and let rest for 10 minutes. Slice thinly against the grain.