Place the tuna steaks on a large plate and thickly crust them with cracked peppercorns, pressing the pepper onto the fish on both sides and the edges. Generously season the tuna with Old Bay seasoning and salt. Place the olive oil in a shallow bowl.

Set up the grill for direct grilling and preheat it to high.

When ready to cook, brush and oil the grill grate. Dip each piece of tuna in the olive oil on both sides, then arrange it on the hot grate. The dripping oil may and should cause flare-ups—it's supposed to. The flames will help sear the crust.

Grill the tuna until it is dark and crusty on the outside but still very rare inside, 2 to 3 minutes per side, turning with tongs. When done the tuna should feel quite soft when poked.

Transfer the grilled tuna steaks to a cutting board and cut them into 1/4-inch slices. Cut down through the steaks, holding the blade perpendicular to the cutting board. Each slice will have a dark crusty exterior and a blood-rare center. Fan out the slices on a platter or plates.

Garnish the tuna with lemon or lime wedges and serve the bowls of dipping sauce alongside.