At least 2 hours and up to 1 day before serving, rinse the tuna. Pat dry. Cut into 2-inch-by-½-inch-by-½-inch strips; spread out in a single layer on a baking sheet. Chill, uncovered, for 2 hours or up to 1 day. (If longer than 2 hours, top with parchment paper.)
Up to 1 hour before serving the ceviche, peel the avocado and radishes and slice as thinly as possible. Cut the avocado into bite-size pieces and layer between 2 sheets of plastic wrap to prevent browning; refrigerate. Place the radishes in a bowl of ice water.
To the leche de tigre, whisk in the soy sauce, sesame oil, wasabi paste, and togarashi, if using.
To serve, add the tuna and a pinch each of salt and white pepper to a chilled bowl. Let stand for 30 seconds, then add the cilantro and stir for 10 seconds. Stir in the shallot and ají limo or habenero.
Transfer the fish to a cold plate, and garnish with the avocado and radish slices, puffed rice, and seaweed, if using. Serve immediately, pouring the liquid over the fish at the table.
