Preheat oven to 350° F. Grease a 1-½- to 2-quart covered casserole. In a medium bowl, combine the onion. ham, ½ cup Parmesan cheese, and thyme or dill. Arrange a layer of potato slices in the bottom of the casserole. Sprinkle generously with salt and pepper. Sprinkle a layer of the ham mixture over the potatoes. Repeat the layers two more times, each time generously seasoning the potato slices with salt and pepper. End with potatoes. Pour the milk over the layers, up to the top layer of potatoes. Sprinkle on the remaining ¼ cup Parmesan cheese. Cover and bake for 45 minutes. Remove the cover and bake for 15 minutes longer, or until the potatoes are tender and the top is golden brown.