Pat the steak dry and trim any silverskin. Lightly score the surface in a shallow crosshatch (about 1/8-inch deep) to help the marinade penetrate. Place the meat in a large zip-top bag or shallow glass dish.
Whisk together all marinade ingredients until smooth. Set aside 2 tablespoons of the marinade in a small saucepan for finishing; pour the remainder over the steak, seal, and massage to coat, working it into the scores.
Refrigerate the steak 4–12 hours, turning once or twice. For a stronger flavor, marinate up to 24 hours.
Remove the steak from the marinade, letting excess drip off; discard used marinade. Pat very dry with paper towels and set on a wire rack. Let it stand at room temperature for 20–30 minutes while you preheat your cooking method.
To broil: Position an oven rack 6 inches from the broiler and preheat the broiler on high. Set a rimmed sheet pan or broiler pan under the heat for 5 minutes to preheat. Place the steak on the hot pan and broil 5–6 minutes. Flip and broil another 4–6 minutes, until an instant-read thermometer inserted in the thickest part reads 130–135°F for medium-rare (135–140°F for medium).
To grill: Preheat a gas or charcoal grill to 500°F (hot fire). Clean and oil the grates. Grill the steak 5–7 minutes, covered, then flip and grill 4–6 minutes more, aiming for 130–135°F in the center for medium-rare (135–140°F for medium).
Transfer the steak to a cutting board and rest 10 minutes, loosely tented with foil. Meanwhile, bring the reserved clean marinade to a lively simmer in the small saucepan for 2–3 minutes to make a quick drizzle.
Slice the steak thinly against the grain at a 45° angle. Spoon over a little of the reduced marinade, scatter with chopped parsley, and serve immediately.