In blender or mini chopper, combine mayonnaise, lemon juice, Parmesan, garlic, anchovy paste and 1/4 teaspoon each of the salt and pepper. Cover blender and run until mixture is smooth and garlic is pureed. With blender running, add olive oil in a thin stream. Set aside.
Season beef with remaining 1/4 teaspoon each salt and pepper. Heat cast iron skillet or grill pan over medium-high heat.
Toss romaine leaves with dressing in large bowl (do in batches, if necessary). Grill or pan-roast beef for 4 to 6 minutes per side, depending on thickness, until meat registers 135 degrees F on instant-read thermometer for medium-rare. Grill another minute per side for medium. Remove to cutting board and cover with foil.
Divide lettuce among plates. Slice steak and place alongside salad.
