Combine the soy sauce, mirin, vinegar, ginger, garlic and brown sugar in a bowl and whisk together well. Add the sesame oil and blend.
Place the tuna and marinade to a large zip-top bag and refrigerate for 1 to 2 hours.
Prepare a hot grill, or heat a heavy cast-iron or nonstick skillet over medium-high heat. Remove the fish from the marinade. Reserve marinade. Cook the steaks for 2 to 4 minutes on each side depending on thickness of tuna. Remove tuna from pan to plates. Return marinade to hot pan til it bubbles. Drizzle hot sauce over tuna.