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1
Preheat oven to 450 degrees F (230 degrees C). Grease a large baking pan with olive oil.
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2
Pierce potatoes and sweet potatoes all over with a fork. Place in the baking pan.
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3
Bake in the preheated oven until tender, about 1 hour. Cut hot potatoes in half, holding them with a towel to protect your hands.
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4
Dust a flat work surface with flour using a sifter. Press potatoes through a potato ricer directly onto the work surface. Sprinkle 1/4 cup Parmigiano-Reggiano cheese, salt, and pepper evenly over potatoes. Mix well.
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5
Drizzle egg yolk over potato mixture; knead in by hand or with a bench scraper. Sift in flour gradually until potato mixture is smooth and slightly sticky, adding more flour as needed. Form into a ball; sprinkle flour over the top. Divide dough into 5 small balls. Dust each ball lightly with flour.
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6
Roll each ball of dough into a 1/2-inch rope. Cut each rope into 1/2-inch gnocchi. Transfer gnocchi to a baking sheet lined with parchment paper. Repeat with remaining dough. Roll gnocchi over the tines of a fork or a gnocchi board to create ridges.
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7
Bring a large pot of salted water to a rolling boil. Cook gnocchi in batches until they rise to the surface, 3 to 4 minutes per batch. Transfer to a baking pan using a slotted spoon. Let cool.
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8
Cook 'nduja in a skillet over medium-low heat until it has a loose, spoonable consistency, 3 to 5 minutes. Add butter; cook until foamy. Add sage; cook until butter starts to brown and leaves are crisp, about 3 minutes. Remove from heat. Transfer sage to a plate and stir in balsamic vinegar. Let sauce cool slightly.
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9
Spoon gnocchi into the skillet with the sauce. Cook over low heat, stirring constantly, until gnocchi are heated through and coated with sauce, about 5 minutes. Plate the gnocchi and top each serving with fried sage leaves, 1 tablespoon balsamic glaze, and 1 tablespoon Parmigiano-Reggiano cheese.
