Pat the tuna fillets dry with kitchen paper and add to a mixing bowl with the soy sauce, sesame oil, lime juice, and sliced ginger. Leave the tuna to marinate for 15 minutes. The marinade can also be saved and used in a number of other recipes, including as a sauce for stir fried vegetables or fried rice.
Once the tuna has marinated, heat a heavy-bottomed frying pan over medium-high for 2-3 minutes. Remove the tuna fillets from the marinade and scrape off as much ginger as possible to prevent it from burning. Add the tuna to the pan and cook, undisturbed, for two minutes. Flip the tuna fillets over and cook for another minute or two, until all sides are lightly seared.
Remove from the pan (or cook for longer if you prefer the tuna to be well done) and serve garnished with chopped spring onion greens.