Cut potatoes into 1/8-inch thick slices; place in a bowl of lightly salted water. Set aside.
Fill a medium Dutch oven one-fourth full of water; bring to a boil. Drain potatoes; add to boiling water. Cover and cook over medium heat 20 minutes or until tender; drain well and set aside.
Melt 1/4 cup plus 1 tablespoon butter in a medium saucepan; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Add salt and pepper; stir well.
Alternate layers of white sauce, potatoes, cheese, and parsley in a greased shallow 2 1/2- quart casserole, beginning and ending with sauce. Sprinkle top with breadcrumbs and dot with 2 tablespoons butter. Cover and bake at 350° for 15 minutes or until thoroughly heated.