1. Turn on all burners to high, close the lid, and heat the grill until very hot, about 15 minutes. Scrape the grill grate clean with a grill brush. Leave on all burners on high. Grill the tuna, covered and turning once (using a metal spatula), to the desired doneness, 5 to 6 minutes for rare or 7 to 8 minutes for medium-rare. Serve immediately.
1. Light a large chimney starter filled with hardwood charcoal (about 6 quarts) and allow to burn until all the charcoal is covered with a layer of fine gray ash. Build a single-level fire by spreading the coals out evenly over the bottom of the grill. Set the cooking rack in place, cover the grill with the lid, and let the rack heat up, about 5 minutes. Use a wire brush to scrape clean the cooking rack. The grill is ready when the coals are medium-hot. (see hot to gauge heat level on page 568.)
2. Cut the tuna steaks in half to make four equal pieces. Brush the tuna with the olive oil and generously sprinkle with salt and pepper.
3. Lightly dip a small wad of paper towels in vegetable oil; holding the wad with tongs, wipe the grill rack (see page 616). Grill the tuna, uncovered and turning once (using a metal spatula), to the desired doneness, 4 to 5 minutes for rare or 6 to 7 minutes for medium-rare. Server immediately.