Tip:To make mini cakes, simply portion the mixture into 24 small mounds, shape into cakes, and press a small cilantro leaf on each one. Cook as directed in the recipe.
Grind the star anise in a clean electric coffee grinder.
Heat 2 Tbs. of the oil in a large nonstick skillet over medium-high heat. Add the shiitakes and sauté, stirring as needed, until cooked through, golden, and slightly crisp around the edges, 5 to 7 min. Transfer to a cutting board, let cool, and then coarsely chop.
Coarsely chop the shrimp and transfer to a large bowl. Put the scallops in a food processor and purée until smooth. Add the scallops to the bowl of shrimp. Add 1 tsp. of the star anise, along with the shiitakes, mirin, cilantro, scallions, sesame oil, and 1/2 tsp. kosher salt. Combine well using a rubber spatula—don’t worry about overmixing. Cover the bowl and chill for 30 min. or more. Discard any remaining ground star anise or save for another use.
Turn the mixture out onto a baking sheet and portion it into eight equal mounds. With wet hands, shape each mound into a flattened cake about 2-1/2 inches wide and 1/2 inch thick. Press a cilantro leaf, nice side up, onto the top of each cake.
Heat the oven to 200°F. Heat 1 Tbs. of the oil in a large nonstick skillet over medium heat. Using a rubber spatula, transfer four of the cakes to the pan with the cilantro-leaf side down. Cook until lightly browned on both sides and cooked through, turning once or twice with a spatula, 5 to 6 min. total cooking time. Transfer to a plate, cover, and keep warm in the oven. Wipe the skillet clean and then cook the remaining cakes as above, using the remaining 1 Tbs. oil.
Serve hot, with ramekins of the Gingered Soy Sauce for dipping.