Chop the tuna into chunks, add them to a food processor, and pulse a few times to break up the pieces. In a bowl mix the soy sauce, oil, lime juice, cilantro, and ginger; season with salt and pepper. Pour over the tuna and process until well blended. Form into 4 patties and grill.
For the sauce, cut the tofu into chunks and put them into a blender with the ginger, cilantro, chile, sesame oil, lime juice, soy sauce, water, and salt and pepper, to taste. Puree, taste, and adjust seasoning. Top the burgers with the sauce and garnish with the spicy sprouts.