Even with cleaned squid, you’re going to have to do a bunch of stuff to it: Rinse the squid well under running water (fig. 1.1). Pull off and discard the wings (fig. 1.2), feel around in the tubes, pull out any gunk, and rinse it away. Cut the tubes into ½-inch rings (fig. 1.3) and rinse them in a bowl of water. Drain, dry on paper towels, turn into a bowl, cover, and refrigerate until ready to use.

Heat 2 tablespoons of the olive oil in a heavy-bottomed 4-quart sauté pan or rondeau over medium-high heat. Add the squid and sauté until the rings are opaque, about 2 minutes. Sprinkle with ½ teaspoon salt and ½ teaspoon pepper. Using a slotted spoon or wire skimmer, transfer the squid to a bowl, leaving the juices in the pan. Add the remaining 1 tablespoon olive oil and the onion to the pan and sauté over medium heat until the onion is soft and fragrant, about 5 minutes. Add the ginger and garlic and sauté, without allowing the ingredients to color, until softened and fragrant, about 5 minutes more. Return the squid to the pan and pour in the ½ cup white wine (fig. 2.1). Add the hot fish stock, marjoram, bay leaf, and red pepper flakes. Stir and cover. Bring to a simmer, and then reduce the heat and simmer gently, stirring occasionally, until the squid is tender, about 1 hour (fig. 2.2). 

While the squid braises, turn the mussels into a colander in the sink and rinse them under cold running water. Scrub the shells with a brush and tug off and discard any fuzzy beards that protrude from them. If a mussel shell gapes open, rap it sharply; if it doesn’t close, discard the mussel.

When the squid has finished cooking, transfer it with the slotted spoon or wire skimmer to a bowl, leaving the braising liquid behind. Turn the cleaned mussels into the pan, increase the heat to high, cover, and steam the mussels until they open (fig. 4.1), 5 to 7 minutes. Remove the pan from the heat. Using the slotted spoon, transfer the mussels to the colander set over a bowl to collect the juices. Let cool slightly, and then remove the mussels from their shells (without breaking the hinges), tossing the meats into the bowl with the squid (fig. 4.2). Reserve 24 of the nicest hinged shells, wash them under running water, and set aside. Pour any collected juices from the mussels back into the pan, and then pour the braising liquid through a fine-mesh strainer set over a 2-cup liquid measuring cup. You should have about ½ cup of liquid. Wash the pan, return the braising liquid to it, and bring the liquid to a boil over high heat. Add the remaining 1 tablespoon white wine, the parsley, and butter, and whisk to emulsify. Return the squid and mussels to the sauce and warm briefly (fig. 4.3), about 3 minutes. Taste for seasoning.

Spoon the hot polenta onto six plates or into six shallow bowls. Arrange 4 mussel shells around each serving of polenta and spoon a mussel into each shell. Top with the remaining shellfish and sauce, dividing them evenly. Serve at once.