How to Make It
In a large saucepan, cook the chorizo in the grapeseed oil over moderate heat until the fat is rendered, about 4 minutes. Using a slotted spoon, remove the chorizo, leaving as much of the oil as possible in the saucepan; you should have about 3 tablespoons. Reserve the chorizo.
Add the shallot and chopped fennel to the saucepan and cook over moderately high heat, stirring, until softened, 7 minutes. Add the mussels and wine, cover and cook until the shells have opened, 6 minutes. Transfer the mussels to a large bowl. Strain the cooking juices into a heatproof bowl.
Wipe out the saucepan and return the cooking juices to it, stopping before you reach the grit at the bottom. Add the orange juice, chicken stock and piment d’Espelette to the saucepan and simmer over moderate heat until reduced to 1/2 cup, about 15 minutes. Add 1/4 cup of the olive oil and keep the sauce warm. Remove the mussels from their shells and add them to the sauce.
In a large saucepan, heat the remaining 4 cups of olive oil to 180°. Meanwhile, on a plate, sprinkle the cod all over with the salt; let stand for 5 minutes. Rinse the cod and pat dry. Poach the cod in the oil, adjusting the heat as necessary to keep the temperature constant, until just cooked, 10 minutes. If the cod is not completely submerged in oil, turn it halfway through poaching. Using a slotted spatula, transfer the cod to a paper towel–lined plate and blot dry.
Using a sharp knife, peel the orange, removing all of the bitter white pith. Working over a bowl, cut in between the membranes to release the sections into the bowl. Heat the sauce just until warm. Transfer the cod to 4 shallow bowls and spoon the mussels and sauce all around. Garnish with the orange sections, fennel fronds and fried chorizo and serve.