How to Make It
In a glass baking dish, combine 1/2 cup of the soy sauce with the sake, sugar, scallions and garlic; stir to dissolve the sugar. Add the tuna steaks and turn to coat. Marinate in the refrigerator, turning occasionally, for 1 hour.
Light a grill. Lightly brush the grate with vegetable oil. Remove the tuna from the marinade and pat dry. Brush the tuna with 1 tablespoon of vegetable oil and grill over high heat until lightly browned, about 2 to 3 minutes per side for medium rare. Transfer the tuna to a plate, cover loosely with foil and keep warm.
In a medium bowl, whisk 1 tablespoon of vegetable oil and 1/2 teaspoon of soy sauce with the lime juice and mirin. Season with salt and pepper. Add the carrots, cucumber, radish sprouts and onion and toss to combine. Mound the slaw on 4 dinner plates. Thickly slice the tuna and arrange it over the slaw. Pour any accumulated juices over the tuna and serve.