Besides their wonderful flavor, one of the things that’s remarkable about tuna steaks is simply how great they look, especially with grill marks on the outside and a nice brown crust concealing a tender, still-red interior. And tuna steaks really hold their shape after grilling; no falling-apart flakiness here. To achieve those beautiful grill marks, you need to leave the steaks alone for a couple minutes; don’t turn or move them, at all. Resist the temptation to tamper, and just let them alone. And to get that perfectly seared outside while maintaining a nice rare (or even raw, if that’s your preference) interior, just pop your steaks in the freezer for an hour before you grill.
Prepare a Charcoal or gas grill for medium-high heat or preheat a ridged grill pan over a medium-high flame. Wash and pat the tuna dry with paper towels. Brush both sides of the tuna with the oil and sprinkle with the salt and pepper. Grill the tuna until just seared on the outside but still rare in the center, about 2 minutes per side. If desired, continue cooking the tuna until just cooked through in the center, about 2 minutes longer per side. Using a metal spatula, transfer the tuna to a cutting board and set aside for 5 minutes.
Using a large, sharp knife, cut the tuna across the grain and on a bias into ½-inch-thick slices. Arrange the slices on a serving plate. Drizzle with the lemon juice, and serve with the basil pesto.