Make the topping: In a bowl, combine the breadcrumbs, melted butter, and a pinch of salt. Mix in the mustard and then the Parmigiano and parsley.
Prepare the gratin: Preheat oven 350. Rub shallow 2-quart gratin dish with butter, set aside.
Melt 2 TBS butter in a saucepan over medium heat. Add shallots and pinch of salt; cook, stirring frequently, until softened, limp and somewhat golden. Whisk together the cream, broth, and horseradish; add to the shallots. Season with salt and pepper, stir to combine, and take the pan off the heat.
Assemble the gratin: In a large bowl, combine the potato and sweet potato slices with salt, Parmigiano and the shallot cream. With a rubber spatula, mix gently but thoroughly and scrape into the prepared gratin dish, smoothing and pressing until evenly distributed.
Bake the gratin: Cover with the breadcrumbs. Bake until the crust is deep golden brown, the juices around the edges have subsided, and the potatoes are tender when pierced with a fork, about 1 hour.