Let the steak stand at room temperature for 30 minutes.

Strip the leaves from 6 thyme sprigs.

Finely chop the thyme leaves to yield about 1 tablespoon.

Set the chopped thyme aside.

Place half of the remaining thyme sprigs in a small bowl.

Cover the thyme with cool water and soak for 10 minutes while heating the grill.

Preheat a gas or charcoal grill to medium-low.

Pat the steak dry and rub both sides with the chopped thyme, salt, and pepper, pressing to adhere.

Drizzle both sides of the steak with olive oil.

Rub the grill grates with oil to prevent sticking.

Place the steak on the grill, close the lid, and grill for 8 minutes for medium-rare.

Lift the grill grate and toss half of the soaked thyme sprigs directly onto the gas burner or coals to create smoke.

Rotate the steak a quarter turn to create grill marks.

Close the lid and cook the steak for another 8 minutes.

Lift the lid and set the remaining soaked thyme on the fire.

Turn over the steak and cook for 8 minutes.

Rotate and cook for 8 minutes more.

Check the internal temperature of the steak with an instant-read thermometer (125°F for medium-rare).

Transfer the steak to a cutting board and let it rest for 10 minutes before carving.

Cut the meat away from the bone and set the bone on a serving platter.

Cut the steak into 1/4-inch-thick slices.

Arrange the slices around the bone.

Scatter the remaining thyme sprigs on top.