Step 1Heat a grill over medium-high heat. (It will be hot enough when you can hold your hand an inch over the grill for only 5 to 6 seconds.) Lightly oil the grill, and place the steak on the grill. Grill the steak for 5 minutes, then flip over and grill the other side 5 more minutes.
Step 2Carefully place the steak vertically on the grill, so it is resting on the flat part of the T-bone. Continue to cook, allowing the heat to transmit through the bone to the meat. Cook an additional 15 to 25 minutes (this will depend on the heat of your grill) until a thermometer inserted reads 125 degrees for medium-rare. Remove the steak from the grill to a plate and allow it to rest for 2 to 3 minutes.
Step 3Lightly season the steak with the salt and a couple grinds of pepper, then drizzle the olive oil over it. Slice the steak away from the bone, and then crosswise into strips. Serve immediately.