Combine flour and 1/2 cup milk, stirring until smooth. Combine flour mixture, remaining 1 1/4 cups milk, mustard, pepper, and salt in a medium saucepan, stirring well. Cook over medium heat, stirring constantly, until milk mixture is thickened and bubbly. Remove from heat; add cheese, stirring until cheese melts. Stir in sour cream.
Combine cheese mixture, ham, and hash browns in a large bowl, stirring well. Spoon potato mixture into a 13- x 9- x 2-inch baking dish coated with cooking spray. Cover and bake at 350° for 30 minutes. Uncover and bake 30 to 35 additional minutes or until golden.