Ensure the ahi tuna steaks are thawed if previously frozen. Pat them dry gently with paper towels to remove excess moisture.

In a bowl, combine the freshly squeezed Key lime juice, Tamari soy sauce, cold-pressed toasted sesame oil, and the thinly julienned fresh ginger. Mix the ingredients thoroughly to create the marinade.

Place the ahi tuna steaks in a shallow, non-reactive dish or a large zip-lock bag. Pour the marinade over the tuna steaks, ensuring they are fully coated. Cover the dish or seal the bag tightly. Refrigerate for at least 30 minutes to allow the flavors to infuse into the tuna.

Preheat your grill to high heat or a skillet on the stovetop over medium-high heat. Ensure the grill grates or skillet are well-oiled to prevent sticking.

Remove the marinated tuna steaks from the refrigerator and allow them to come to room temperature for about 10 minutes.

Sprinkle the coarsely ground Tellicherry black pepper evenly on both sides of each tuna steak.

Place the tuna steaks on the preheated grill or skillet. For a 1-inch thick steak, grill for approximately 1-2 minutes per side for rare to medium-rare doneness, depending on your preference. Ensure not to overcook the tuna, as it should remain tender and slightly pink in the center.

Once cooked to your desired level, remove the tuna steaks from the heat and let them rest for a few minutes. Then, using a sharp knife, slice the tuna against the grain into thin, even slices.

Arrange the sliced tuna on a serving platter, garnish with additional fresh ginger if desired, and serve immediately.