Place stockfish in a large bowl or pot and cover with cold water, then place in refrigerator for 4–5 days, changing water at least 3 times a day, and more often if possible, until fish is rehydrated and soft.
Bring a large pot of water to a boil over high heat. Drain stockfish and cook, just until flesh is tender and flakes easily, 8–10 minutes. Drain, reserving 1 cup of the cooking water.
While fish is still warm, remove and discard bones, reserving skin and stomach membrane (these help give the finished dish its creamy texture). Tear flesh, skin, and membrane into small pieces and put into a sturdy bowl or the bowl of a standing mixer fitted with a paddle. Add anchovies and garlic.
Beat fish vigorously with a wooden spoon or beat on medium-low speed with mixer, while slowly drizzling in just enough oil (about ½ cup), to make the mixture light and creamy, about 30 minutes. Beat in a little reserved cooking water if baccalà is too dry. Season to taste with salt. Serve garnished with chopped parsley and Grilled Polenta, if you like.