Grease a 13x9x2 inch baking dish with 2 tablespoons butter. Arrange fish in the baking dish. Set aside.
Place potato strips in a large saucepan with water to cover. Bring to a boil, reduce heat, and simmer 2 minutes or until the potato is almost tender. Drain well, pat dry with paper towels. Return the potato strips to the saucepan. Add 2 tablespoons butter, tossing gently until butter melts. Set aside.
Melt the remaining 3 tablespoons butter in a heavy saucepan over low heat; add flour and mustard, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add the milk; cook over medium heat, stirring constantly, until the mixture is thickened and bubbly. Stir in salt and pepper to taste.
Spoon the sauce evenly over the fish in the baking dish; arrange the potato strips over the sauce. Sprinkle with the shredded cheese. Bake at 400 degrees for 30 minutes or until the cheese melts and the mixture is hot and bubbly. Serve immediately.