In a bowl, whisk the mayonnaise, soy sauce, sesame oil and 2 tablespoons of the Sriracha.
In a food processor, pulse one-third of the tuna at a time just until finely chopped; transfer to a bowl. Repeat with the remaining tuna.
Light a grill or preheat a grill pan. Mix the Chinese mustard, garlic, 2 1/2 teaspoons of salt and 1/2 teaspoon of pepper into the chopped tuna. Using lightly moistened hands, form the tuna into six 4-inch burgers. Brush with oil and season with salt and pepper. Grill the burgers over high heat, turning once, until lightly charred on the outside and rare in the center, about 3 minutes total.
Spread both halves of the buns with the Sriracha mayonnaise. Set the burgers on the buns and top with the pickled ginger. Drizzle 1 1/2 teaspoons of the Soy Glaze and 1/2 teaspoon of Sriracha on each burger. Top with scallions, lettuce and tomatoes and serve.