Preheat oven to 350°F. In a 4-quart Dutch oven cook potatoes in enough boiling lightly salted water to cover about 10 minutes or just until tender; drain and set aside.
Meanwhile, in a medium bowl toss together cheese and flour; set aside. In another medium bowl whisk together broth, whipping cream, mustard, salt, thyme, and pepper; set aside. In a small bowl combine bread crumbs and melted butter.
In a 3-quart rectangular baking dish layer half of the potatoes and half of the cheese mixture. Repeat layers. Pour broth mixture evenly over layers in baking dish. Sprinkle with bread crumb mixture.
Bake, uncovered, about 35 minutes or until potatoes are tender and sauce is bubbly. Let stand for 10 to 15 minutes before serving. If desired, sprinkle with parsley.