In a shallow bowl, add the black and the white sesame seeds. Pat the tuna very dry. smear a bit of wasabi paste on both sides of the fish. Season the fish with salt and pepper.
Heat a frying pan over medium-high heat and add the cooking oil. When the oil is shimmering, carefully lay the tuna fillets in the pan, not touching. Cook for 2 minutes then flip the tuna. Cook 2 minutes, then flip the fillets to its side to cook 1 minute. Flip one more time to cook the other side for 1 minute so that you have a good sear on all sides, taking care not to burn the sesame seeds. If the seeds start turning brown too quickly, lower the heat. Remove the fish to a plate.
In a small bowl, whisk together the lime juice, ginger and the oil. Season with salt and pepper to taste.
Slice the fish into thin slices and arrange on a plate. Drizzle some of the lime-ginger vinaigrette over the fish. Toss the remaining lime-ginger vinaigrette with salad greens, if desired.