Pluck and discard the outer leaves of the artichokes, revealing yellow-green core. Using a serrated knife, trim off the top third. Cut each into quarters. Bring medium saucepan of water to a boil. Add artichokes and cook 2 minutes. Drain and pat dry. Transfer to a bowl and toss with 2 T. oil. Season with salt and pepper to taste. Preheat oven to 400 and preheat a cast iron skillet until very hot. If your fire alarm is as sensitive as mine, get that oven vent on high! Season steak with salt and pepper. Add remaining 1 T. oil to pan and add steak, garlic and herbs. Cook over high heat until steak is brown and crusty on bottom and sides, about 10 minutes. Flip and set garlic and herbs on top. Add artichokes to skillet around the meat. Place in oven and roast until steak reaches 135 in the center, about 20 minutes. Transfer to cutting board and let rest 10 minutes. Strip rosemary and thyme leaves from stems, discard stems and add leaves to artichokes. Thinly slice steak and arrange on platter, surround with the artichokes and garnish with shaved parmesan.