Press cooked rice into a lined tray, drizzle with mirin if using, cover, weight down, and refrigerate overnight until firm. Cut into rectangles and refrigerate uncovered until dry. Pan-fry in hot oil until deeply golden and crisp. Season with salt and togarashi.
Blend avocado, water, lemon juice, jalapeño, and salt until smooth and spoonable. Adjust seasoning and set aside.
Slice remaining avocado into thick wedges and coat evenly in puffed rice togarashi.
Lightly oil and season tuna with paprika and salt. Sear in a very hot pan for 5–10 seconds per side, just to form a crust. Slice cleanly.
Dress frisée with lemon, olive oil, and salt. Arrange rice cakes on a chilled plate, top with tuna, and scatter avocado wedges. Spoon avocado emulsion in the center, swirl with olive oil, and finish with flaky salt and pickled red onions.