6 ounces baked ham, sliced 1/4 inch thick and cut into 1/4-inch cubes
Preheat the oven to 400° and butter a shallow 9-by-13-inch baking dish. In a medium saucepan, bring the heavy cream to a simmer. Add the garlic and nutmeg and season with salt and pepper. Keep warm.
Using a mandoline, slice the potatoes crosswise 1/8 inch thick. In a small bowl, combine the pecorino and Parmigiano cheese. Arrange one fourth of the potato slices in the prepared baking dish, overlapping them slightly. Sprinkle 1/4 cup of the cheese, 1 tablespoon of the parsley and one third of the ham over the potatoes. Repeat the layering two more times. Top with a final layer of potatoes and sprinkle with the remaining 1/4 cup of cheese. Pour the cream mixture over and around the potatoes.
Bake for 25 to 30 minutes, until the potatoes are tender and bubbling and the top is golden brown. Let stand for 15 minutes. Sprinkle with the remaining 1 tablespoon of parsley and serve.
The unbaked gratin can be refrigerated overnight. Return to room temperature before baking.