Put the smoked fish in a pan and cover with water. Bring to a boil over medium heat and cook for 10 minutes. Remove from the pan and drain. Remove the skin and bones and flake the fish. Heat 3 tablespoons of butter in a saucepan, stir in the flour, and cook gently 2 minutes, continuing to stir. Off heat, add the milk, then return to the heat and stir constantly, until the sauce thickens.
Add salt and pepper to taste, reduce heat and simmer, stirring often, for about 12-15 minutes. Combine the flaked fish with the sauce, and add the potatoes and the dill. Pour the mixture into a shallow baking dish and dot the surface with the remaining 1 tablespoon butter. Bake in a preheated 350 degree oven for about 15 minutes, until lightly browned. Sprinkle with chopped parsley.