Heat a griddle or cast-iron skillet over medium-high heat. Season the steaks with salt and pepper and coat with some EVOO. Cook the steaks, turning once, for 10 minutes. Transfer to a cutting board and let rest for 10 minutes, then thinly slice on an angle.
In a salad bowl, combine the lemon juice, garlic, anchovy paste, worcestershire and mustard; season heavily with pepper. Using a fork, mix in the egg yolk, then pour in 1/3 cup EVOO in a slow, steady stream to emulsify the dressing. Stir in a handful of cheese. Add the kale and romaine and toss to coat. Serve the salad topped with shaved cheese, alongside the steak.