How to Make It
Preheat the oven to 425°. In a small bowl, mix the salt with the sugar. Spread half of the salt in the bottom of a shallow bowl that just holds the cod. Lay the pieces of cod on the salt and sprinkle the remaining salt on top. Cover with a plate and weight it down with a large, heavy can. Let stand at room temperature for 30 minutes or refrigerate for up to 4 hours. Rinse the cod pieces and pat them dry.
Meanwhile, stand the peppers on a rimmed baking sheet, rounded side up. Bake for about 25 minutes, or until the skins are blistered. When the peppers are cool enough to handle, peel them and gently tear each one in half lengthwise.
In a medium saucepan, simmer the olive oil with the garlic and chile over moderate heat until the garlic is golden, about 3 minutes. Add the cod and simmer over low heat until it is just cooked, 3 to 4 minutes per side. Transfer the cod to a bowl. Strain the oil through a coarse sieve into a glass measuring cup; reserve the garlic and chile.
Break up the cod into small flakes and season lightly with table salt if needed. Cut four 8-inch squares of plastic wrap. Lightly oil 1 sheet and lay 2 pepper halves on it, shiny side down, overlapping slightly. Shape one-fourth of the cod into a tight ball and set it in the center of the pepper. Wrap the cod in the pepper, twisting the plastic wrap around the pepper to give it a neat round shape. Transfer to a plate, twisted end down. Repeat with the remaining peppers and cod.
In a blender, puree the sherry vinegar with the reserved garlic and chile. With the machine on, slowly pour in the reserved garlic oil until emulsified. Season with salt and pepper.
Put the cod packages in a microwave oven and cook at high power for 1 minute, or until the cod is just hot in the center. Carefully unwrap each package and transfer the peppers to plates. Spoon the sauce over the peppers, sprinkle with parsley and serve.