Sweet Potato Gnocchi with Fried Sage and Shaved Chestnuts

INGREDIENTS

• 1 (3/4-pound) sweet potato
• 1/3 cup extra-virgin olive oil
• 1 1/2 to 2 cups all-purpose flour plus more for dusting
• 1 1/4 pounds russet (baking potatoes)
• 1/3 cup grated Parmigiano-Reggiano plus more for serving
• 2 tablespoons unsalted butter
• 1/2 teaspoon grated nutmeg
• 1 large egg
• 1/3 cup bottled roasted chestnuts, very thinly sliced with an adjustable-blade slicer or a sharp vegetable peeler
• 1 cup sage leaves (from 1 bunch)