Mix the thyme, salt and pepper in a small bowl. Grate the cheddar cheese and mix lightly with the flour. In another bowl, mix the cream, broth and mustard.
Cover the bottom of a buttered backing dish with a layer of potatoes. Sprinkle 1/3 of the spices, ham and cheese. Put down another layer of potatoes, then another third of the spices, ham and cheese. One final layer of potatoes, spices, cheese and ham.
Pour in the liquid and bake at 350° for 30 minutes.
Meanwhile, brown the bread crumbs lightly in a skillet with the butter. Sprinkle them over the potatoes and bake another 45 minutes. Let the dish stand for 5 or 10 minutes before serving.