Combine soy sauce, sesame oil, ginger and garlic in a 13x9 dish. Place the tuna steaks into the marinade and coat evenly. Cover with plastic and keep in the fridge for about 40 minutes.
Heat the canola oil in a large pot several inches from the bottom. When the oil reaches 375 degrees, drop a wonton square into it and let it cook for about 40 seconds and then flip it over for another 20 seconds. Transfer to a plate with a paper towel on it. Repeat this process to make as many wonton strips as desired.
Add the wasabi powder to a small bowl and using enough water, make a paste. Mix the paste into the mayonnaise. Taste and adjust if necessary.
In a pan, melt the butter and saute the mushrooms until cooked, about 7 minutes.
Heat the grill on high heat. Sprinkle each tuna steak liberally with sesame seeds. Place each steak on the grill. Grill for about 1½ minutes, flip them over, and then continue cooking for another minute. Make sure you don't overcook the tuna, it should be rare to medium rare.
Spread each bun with wasabi mayo. Place a piece of tuna on top, followed by a couple of wontons, mushrooms and sprouts.