How to Make It
In a small saucepan of boiling water, blanch the basil for 30 seconds. Drain and rinse it under cold running water. Squeeze the excess water from the basil and transfer the basil to a blender. Add the mayonnaise and puree. Transfer to a bowl and season with salt and black pepper. Refrigerate the basil mayonnaise until lightly chilled.
In a large bowl, combine the haddock and shrimp with the panko, heavy cream, egg, chopped parsley and chives, lemon zest, cayenne, 1 1/2 teaspoons of salt and 1/2 teaspoon of black pepper. Form the mixture into eight 1/2-cup cakes, about 3 inches in diameter.
In a large cast-iron skillet, melt 2 tablespoons of the butter in the oil. Add 4 of the fish cakes and fry over moderately high heat until browned and crisp, about 3 minutes per side. Using a slotted spoon, transfer the fish cakes to paper towels to drain. Repeat with the remaining butter and fish cakes, then transfer the cakes to a platter and serve at once, with the basil mayonnaise.