pumpkin or sweet potato gnocchi
1/3 cup extra-virgin olive oil
1 cup sage leaves (from 1 bunch)
1/3 cup bottled roasted chestnuts, very thinly sliced with an adjustable-blade slicer or a sharp vegetable peeler
2 tablespoons unsalted butter
grated Parmigiano-Reggiano plus more for serving
Heat oil in a 12-inch heavy skillet over medium heat until it shimmers. Fry sage leaves in 3 batches, stirring, until they turn just a shade lighter and crisp (they will continue to crisp as they cool), about 30 seconds per batch. Transfer to paper towels to drain. Season lightly with salt.
Fry chestnuts in 3 batches, stirring, until golden and crisp, about 30 seconds per batch. Transfer to paper towels to drain. Season lightly with salt. Reserve oil in skillet.
Add butter to oil in skillet with 1/2 tsp salt and cook until golden-brown, 1 to 2 minutes. Remove from heat.
Add half of gnocchi to a pasta pot of well-salted boiling water and stir. Cook until they float to surface, about 3 minutes. Transfer with a slotted spoon to skillet with butter sauce. Cook remaining gnocchi in same manner, transferring to skillet as cooked.
Heat gnocchi in skillet over medium heat, stirring to coat.
Serve sprinkled with fried sage and chestnuts and grated cheese.