Cook noodles according to package directions, omitting salt and fat.
While noodles cook, lightly spoon flour into a dry measuring cup, and level with a knife. Combine flour and 1/4 cup milk in a heavy saucepan, stirring with a whisk until smooth. Place the pan over medium heat; whisk in 1 3/4 cups milk and mustard. Cook 6 minutes or until mixture begins to thicken, stirring frequently. Reduce heat to low.
Add the cheese, stirring until melted. Stir in the chicken, peas, ham, and black pepper, and serve over noodles.