On a shallow plate, mix together the ginger, sesame seeds, and cracked black pepper. Season the tuna with salt.
Make 1/2-inch deep slices in the tuna, every 1/4 to 1/2-inch or so to make it easier to slice at the end. Roll the tuna in the ginger mixture, pressing lightly so the mixture sticks to the tuna.
Place a saute pan over high heat. Add the oil and sear the tuna on all sides, about 30 seconds per side. Remove the tuna from the pan and set aside. Deglaze the pan with lime juice. Pour the lime juice over the tuna.
In a bowl combine the avocado, greens, red onion, and tomato. Toss with some of the Ginger Sauce. Slice the tuna, following the incisions made earlier. Place some of the dressed greens on 4 plates. Top with sliced tuna and drizzle with some more of the ginger sauce.
For the ginger sauce - in a small bowl, combine the shallot, ginger, a few grinds pepper, soy sauce, and lime juice. Slowly whisk in the olive oil and set aside. When ready to serve, whisk thoroughly to combine.