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1
Preheat the oven to 350.
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2
Pierce the potatoes all over with a knife, set them on the bottom rack of the oven and bake for about 1 hour, or until tender.
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3
Meanwhile, set the butternut squash, cut side down, on a lightly oiled baking pan.
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4
Cover with foil and bake on the upper rack of the oven for about 50 minutes, or until tender.
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5
Let the squash cool slightly, then peel and cut into 1-inch dice.
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6
Split the potatoes, scoop out the flesh and pass it through a ricer or coarse sieve into a large bowl.
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7
Stir in the egg yolk and 1/2 teaspoon salt.
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8
Add the flour, 1/4 cup at a time, stirring to form a crumbly dough.
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9
Turn the dough out onto a lightly floured work surface and knead until smooth.
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10
Wrap in plastic and let rest at room temperature for 30 minutes.
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11
Line a large rimmed baking sheet with wax paper and dust the paper lightly with flour.
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12
Divide the dough into quarters.
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13
Working with 1 piece at a time and keeping the rest loosely wrapped in plastic, roll each piece into a 1/2 -inch-thick rope.
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14
Using a lightly floured knife, cut the rope into 1/2 -inch lengths.
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15
Spread the gnocchi out on the wax paper and toss to coat with flour.
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16
Roll and cut the remaining gnocchi dough and let stand uncovered at room temperature.
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17
In a large skillet, melt 1 tablespoon of the butter in the oil.
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18
Add the mushrooms, season with salt and pepper and cook over high heat until tender, about 7 minutes.
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19
Transfer to a plate.
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20
Add the remaining 5 tablespoons of butter to the skillet and cook the butter over high heat until golden, 2 to 3 minutes.
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21
Add the lemon juice and sage and cook for 30 seconds longer.
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22
Add the squash and cook, stirring, just until coated with the butter.
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23
Add the mushrooms, season with salt and pepper and keep warm.
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24
Meanwhile, bring a large pot of salted water to a boil.
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25
Add the gnocchi and cook, stirring once or twice, until they rise to the surface and the water returns to a boil, about 1 minute.
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26
Drain the gnocchi and add them to the squash.
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27
Stir to coat with the butter.
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28
Transfer to a large, deep platter and serve immediately.
