Beat the egg in a bowl. Season with salt and pepper. Stir in the cream cheese and/or dill, if you’re using.
Put a small skillet (nonstick is best here) over medium heat for about 1 minute. Add the butter or oil and swirl it around the pan. After the butter melts, but before it foams, turn the heat to low.
Add the egg to the skillet and sprinkle the smoked fish on top. Cook over low heat, stirring occasionally. At first nothing will happen. Don’t lose patience: Keep stirring, breaking up the curds as they form, until the mixture is a mass of soft curds. Serve immediately, sprinkled with pickle salt and/or dill if you’d like.