In a mini chopper or a blender, combine yogurt, Parmesan, lemon juice, anchovies, garlic, 1/4 teaspoon of the salt, and pepper. Puree until smooth and well combined, scraping down side of bowl if necessary. Cut the romaine leaves into thirds and transfer lettuce to a large bowl.
Coat the bottom of a large skillet with oil over high heat. Season steaks with remaining teaspoon salt. Once the oil is hot, place the steak in the skillet. After 3 minutes, flip, and cook the second time for another 3 minutes for medium-rare. Do not move the steak other than to flip. Remove steak and rest 5 minutes.
Pulse dressing again to blend, then toss with lettuce. Divide salad equally among four plates. Thinly slice steak, then fan over salad on each plate, dividing evenly.