3 (1¼ lbs) Yukon gold potatoes
1 (¾ lb) sweet potato
1½ to 2 cups all-purpose flour plus more for dusting
1 large egg
½ teaspoon nutmeg, freshly grated
Freshly ground pepper
1⁄3 cup grated Parmigiano-Reggiano plus more for serving
½ stick unsalted butter
1 cup sage leaves (from 1 bunch)
Roasted chestnuts, shaved
Preheat oven to 450°F. Pierce russet and sweet potatoes in several places with a fork, and bake until just tender, 45 minutes to 1 hour. Cool potatoes slightly, then peel and force through ricer onto sheet pan, spreading in an even layer. Cool potatoes completely. Lightly flour 2 large baking sheets or line with parchment paper. Beat together egg, nutmeg, 1 teaspoon salt and pepper in a small bowl.
Gather potatoes into a mound on sheet pan, and form a well in center. Pour egg mixture into well and knead into potatoes. Knead in cheese and 1½ cups flour, adding more flour as necessary, until mixture forms a smooth, but slightly sticky dough. Dust top lightly with flour. Cut dough into 6 pieces. Form 1 piece of dough into a ½-inch-thick rope on a lightly floured surface. Cut rope into ½-inch pieces. Gently roll each piece into a ball and lightly dust with flour. Repeat with remaining 5 pieces of dough. Transfer gnocchi as formed to baking sheets.
Bring large pot of water to boil, add salt and return to a boil. Working in batches, boil gnocchi until tender, 5 to 6 minutes. Transfer gnocchi to clean, rimmed baking sheet.
Melt butter in heavy large saucepan over medium-high heat. Cook until butter is browned and has a toasty aroma, swirling pan occasionally, about 5 minutes. Add sage. Turn off heat and season sage butter generously with salt and pepper. Transfer half of sage butter to large skillet set over medium-high heat. Add half of the gnocchi. Sauté until gnocchi are heated through, about 6 minutes.
Repeat with remaining sage butter and gnocchi. Divide gnocchi and sauce among shallow bowls. Garnish with sage leaves and shaved roasted chestnuts.