Remove steak from refrigerator and sprinkle with 2 teaspoons salt; let stand 45-60 minutes.
Preheat a cast-iron skillet over high heat until extremely hot, 4-5 minutes. Sprinkle remaining 1 teaspoon salt in bottom of skillet; pat beef dry with paper towels. Place steak in skillet and cook until easily moved, 1-2 minutes; flip, placing steak in a different section of the skillet. Cook 30 seconds and then begin moving steak, occasionally pressing slightly to ensure even contact with skillet.
Continue turning and flipping until cooked to desired degree of doneness (for medium-rare, a thermometer should read 135°; medium, 140°; medium-well, 145°), 1-2 minutes.