Cook potatoes in boiling salted water to cover 35 minutes or until tender. Drain well; cool slightly. Peel and cut into 1/2- inch-thick slices; set aside.
Sauté mushrooms in butter in a medium saucepan until tender. Remove mushrooms with a slotted spoon, and set aside. Reserve butter in pan.
Add flour to melted butter in saucepan, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Stir in reserved mushrooms, 1 cup Cheddar cheese, Parmesan cheese, salt, pepper, and thyme.
Place potatoes in a lightly greased 10- x 6- x 2-inch baking dish. Spoon cheese mixture over potatoes. Sprinkle with remaining cheese and breadcrumbs. Bake, uncovered, at 350° for 30 minutes or until lightly browned. Serve warm.