In a large zip-lock bag, combine the soy sauce, chopped scallions and sesame oil. Mix until combined. Add the tuna steaks and make sure they are well coated. Seal the bag, pressing to remove all air and place on a plate in the refrigerator for 15-20 minutes.
Place the sesame seeds on a plate or a shallow dish. Remove the tuna steaks from the marinade bag, brushing off the scallions if needed. Dip into sesame seeds, patting into steak until all sides are coated.
Preheat your grill to high heat. If you are using a grill basket place that on your grill while heating.
Place tuna steaks on the grill or grill basket and quickly sear, about 1- 1 1/2 minutes per side. Turning carefully with a spatula. Medium rare has an internal temperature of 125 degrees. Warning, it will cook FAST. I find on my outdoor grill I usually end up closer to medium (which is still yummy) vs medium rare on my cast iron on my stove top.
Transfer the tuna to a cutting board and cut into 1⁄4-inch-thick slices. Arrange the tuna on individual plates, overlapping the slices. Serve immediately.