1. Make the marinade: Cook garlic, miso, sake, mirin, soy sauce, and oyster sauce in a pan over medium-high heat, stirring occasionally, for 3 minutes. Transfer to a bowl. Let cool slightly.

2. Using a kitchen mallet, pound both sides of calamari a few times to tenderize. Insert a sharp knife into calamari, cut along seams, and then open like a book. Lightly score inner sides at 1/4-inch intervals. Add calamari to marinade, and let stand for 20 minutes.

3. Make the slaw: Whisk together ginger, vinegar, lime juice, sugar, and salt. Add oil in a slow, steady stream, whisking until emulsified.

4. Preheat grill to medium-high. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 to 4 seconds.) Wrap 3 bricks or the bottom of a heavy skillet with heavy-duty foil. Remove calamari from marinade, and season scored sides with salt. Place calamari, scored sides down, on grill, and top with foil-lined weight. Grill until opaque, about 1 1/2 minutes. Cut into 3/4-inch-wide pieces.

5. Toss celery, apple, scallions, sprouts, and chile with 3 tablespoons dressing (reserve remaining dressing for another use). Arrange on a platter. Top with calamari, and sprinkle with sesame seeds.