Makes 12 cakes
For the fish cakes:
3 tablespoons unsalted butter
1 medium yellow onion, finely diced
1 rib celery, finely diced
1 teaspoon kosher salt + to taste
1 pound boneless, skinless California or Alaska halibut, cut into ¼-inch cubes
1/3 cup heavy cream
1 teaspoon Dijon mustard
½ teaspoon freshly ground black pepper
2¾ cups panko breadcrumbs
¼ cup finely chopped flat-leaf parsley
2 tablespoons finely chopped tarragon
4 large eggs
¾ cup all-purpose flour
Olive oil, for frying
For the sauce:
3 tablespoons mayonnaise
1 hard-boiled egg, finely chopped
1 tablespoon finely chopped parsley
4 cornichon pickles, finely chopped
2 teaspoons capers, finely chopped
2 teaspoons lemon juice
Kosher salt and freshly ground black pepper
To make the fish cakes: In a medium frying pan over medium heat, melt the butter. Add the onions, celery and a pinch of salt and cook, stirring frequently, until softened but not browned, about 10 minutes. Transfer to a bowl and let cool completely.
In the bowl of a food processor combine ½ cup of the diced fish and the heavy cream and process into a smooth paste. Transfer to the bowl with the cooled vegetables and add the remaining diced fish, the 1 teaspoon salt, mustard, pepper, ¾ cup of the breadcrumbs, the parsley, tarragon and 2 eggs. With your hands, mix well to combine. Form the mixture into 12 cakes, each about ¾-inch thick and 3 inches wide. Transfer to a plate or baking sheet and refrigerate for at least 30 minutes or up to 4 hours.
To make the sauce: While the cakes chill, make the sauce. In a small bowl stir together the mayonnaise, egg, parsley, pickles, capers and lemon juice. Season to taste with salt and pepper.
To finish the fish cakes: Preheat the oven to 300 degrees.
In a shallow dish, pour the flour. In a second shallow dish, whisk the remaining 2 eggs. In a third shallow dish, pour the remaining 2 cups breadcrumbs. Coat each fish cake in flour, shaking off excess, then dip in egg, letting excess drip off. Dredge in breadcrumbs, turning twice and patting to adhere. (Note: It’s useful to designate one hand your “dry” hand, the one you use to turn the cakes in the flour and breadcrumbs, and one the “wet” hand, the one you use to turn the cakes in the beaten egg. This way, you avoid breading your fingers, too.) Set on a plate or rimmed baking sheet. Set a wire rack over a second rimmed baking sheet and set nearby.
In a large frying pan, heat ½-inch depth of olive oil over medium heat. When the oil is hot add as many fish cakes as will comfortably fit in a single layer and fry, turning once, until golden brown on both sides and cooked through, about 6 minutes total. With a spatula, transfer the cakes to the wire rack over the baking sheet and keep warm in the oven while you fry the remaining fish cakes, adding more oil to the pan as necessary.
Transfer the fish cakes to a platter and season with salt. Serve warm, accompanied by the sauce.