Preparation

Make the topping:

• Combine the breadcrumbs, melted butter, and a pinch of salt in a bowl. Mix in the mustard and then the Parmigiano and parsley.

Prepare the gratin:

• Heat the oven to 350°F. Rub a shallow 2-quart gratin dish with 1/2 tsp. of the butter. Melt the 2 Tbs. butter in a small saucepan over medium heat. Add the shallots and a big 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 off the heat.

Assemble and bake the gratin:

• Peel the potato and sweet potato, cut each in half lengthwise, and slice each across into thin half moons. In a large bowl, combine the potato and sweet potato slices, 2 teaspoons salt, the 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.Cover with the breadcrumb topping.
• Bake until the crust is deep golden brown, the juices around the edges are have subsided, and the potatoes are tender when pierced with a fork, about 1 hour. Let rest for 15 to 20 minutes before serving.