2 tablespoons peanut oil
1 pound head-on shrimp, peeled and deveined with heads still intact
½ cup sake
1 cup dashi
3 tablespoons sugar
2 tablespoons soy sauce
1-inch piece ginger, peeled and cut into ¼-inch-long strips
2 garlic cloves, thinly sliced
1 fennel bulb, very thinly sliced
1 whole dried red hot chile
¼ cup thinly sliced scallion (white and green parts), divided
One 2-to-2½-pound live lobster
12 cherrystone clams, scrubbed clean
1 pound mussels, rinsed with beards removed
6 tablespoons unsalted butter
Sushi rice, for serving
1. Preheat a large wok over medium-high heat. Add the oil and swirl it around the pan. Add the shrimp in a single layer and sear on one side until lightly browned, 1½ to 2 minutes. Flip and sear the other side for 1 more minute. Transfer the shrimp to a plate and set aside.
2. Add the sake, dashi, sugar, soy sauce, ginger, garlic, fennel, chile and half of the scallions. Bring to a boil. Add the lobster and cook, covered, for 1 minute. Reduce the heat to medium low to maintain a gentle simmer and cook with the lid on for 10 minutes. Turn off the heat and transfer the lobster to a cutting board. When it's cool enough to handle, remove the lobster meat and portion it into 4 bowls. Add the lobster head back into the wok.
3. Place the wok over medium heat. Once the liquid has come to a simmer, add the clams and cook, covered, for 4 minutes. Add the mussels and cook for 2 minutes. Add the reserved shrimp back into the wok and add the butter. Stir the contents of the wok very gently until the butter is fully incorporated, 1 more minute. Discard any clams and mussels that do not open.
4. Divide the clams, mussels and cooked shrimp among the 4 bowls. Pour the broth over the shellfish, making sure to get a little fennel into each bowl. Garnish with the remaining scallions and serve with sushi rice.