Bring a 4-qt. saucepan of water to a boil. Working with 1 piece of tuna at a time, submerge tuna in water for 5 seconds. Using a slotted spoon, immediately transfer tuna to a bowl of ice water and chill for 10 seconds. Remove and pat dry. Repeat with remaining tuna. Place tuna in a plastic bag; add soy sauce, sake, and mirin. Seal; let tuna marinate, turning once, at room temperature for 30 minutes.
To serve, remove tuna from the bag, reserving marinade, and cut each piece into 6 slices. Place 1 cup rice onto 4 serving bowls; top each serving with 6 slices of tuna. Garnish with ginger, nori, shiso, and thinly sliced omelette. Drizzle with reserved marinade; serve with wasabi.