Combine rice, water, ginger, garlic, salt, and butter in a medium saucepot. Cover, boil, then simmer for 15 minutes. Mix seasoning in a bowl. Once water is absorbed, stir in seasoning. Transfer to plastic-lined sheet pan, press to ½ inch thickness with wet hands, and freeze for 5 minutes. Prepare egg wash, cornstarch, and panko. Cut chilled rice into six 3.5-inch circles. Bread: cornstarch → egg → panko. Fifteen minutes before serving, heat oil over medium-high and fry until golden. Drain on wire rack and sprinkle with flakey salt.