When ready to cook, Remove steak to room temperature for at an hour. Rub off marinade. Salt generously.
Light the grill on one side only.
Place steak on side of grill that is not hot.
Turn steak over at 10 minutes. Total grill time in this part of process could take up to 30 minutes. You want to cook low and slow, before searing. Check temperatures below when to switch steak to other side of grill.
For medium rare: Once steak has reached 115 degrees F, move to side of grill that is lit. Cook until temperature reaches 135 F. For medium, remove steak to hot side of grill at 125 degrees F. Cook until temperature reaches 145 F. Grill on each side 1 to 2 minutes on high. Using tongs, hold fat edge over the grill to brown it also.
Remove to plate, top with thyme butter and allow to rest for ten minutes.
Cut steak across the bone in two inch slices.
Season as needed with salt and pepper.