Prep Time: 40 minutes
Cook Time: 20 minutes
Cook sweet potatoes in simmering water until very tender, 16 to 18 minutes. Drain well; transfer to a large bowl. Mash well with potato masher; let stand until cooled to room temperature, about 10 minutes.
Stir in egg, salt and nutmeg; mix well. Stir in 1/4 cup cheese. Stir in flour 1/4 cup at a time until soft dough forms. Divide dough into 4 pieces. On a floured surface, roll each piece of dough to form a 1/2-inch thick long rope. Cut rope into 1 inch pieces; roll each piece with well-floured hands to form a smooth oval shape and place on a sheet of waxed paper.*
Bring a large pot of water to a boil; add 1 tablespoon salt. Add half of gnocchi to water; simmer until tender, 4 to 5 minutes, stirring once. Transfer with slotted spoon to clean sheet of waxed paper; cool completely. Repeat with remaining gnocchi. Gnocchi may be made through step 3 up to 2 ours in advance; let stand at room temperature. Gnocchi may also be covered and chilled up to 24 hours or frozen up to 3 months.
Melt butter in a large deep skillet over medium heat. Cook until butter begins to brown and has a nutty aroma, about 4 minutes. Stir in sage; reduce heat to medium-low. Add gnocchi; sauté until heated through, 4 to 5 minutes. Spoon into shallow bowls; top with remaining cheese.