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1
Preheat oven to 350 degrees.
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2
Using a chestnut knife or a small paring knife, make an incision about 1/8 inch deep through the shell and into the flesh of each chestnut almost all of the way around the circumference of the nut.
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3
Transfer to chestnut pan or rimmed baking pan.
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4
Roast in the oven until the chestnuts are tender, about 35 minutes.
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5
Turn the oven off.
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6
Leaving the pan with the chestnuts in the oven, remover several at a time.
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7
Working quickly, place one chestnut in a towel and holding both, peel the chestnut while still hot.
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8
Immediately remove and discard the shells and inner skin.
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9
Break into halves or quarters; set the chestnuts aside.
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10
Place a large pot of water over high heat.
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11
In a large high sided saute pan, melt butter and olive oil over medium heat.
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12
Add the leeks and the garlic, and cook, stirring occasionally, until softened, about 6 minutes.
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13
Add chestnuts and squash, season with salt and pepper.
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14
Cook until tender, 15 to 20 minutes.
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15
Add vermouth and stock, raise heat to medium high and cook until liquid is reduces by little more than half, about 2 minutes.
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16
Meanwhile, add salt and pasta to the large pot of boiling water, and cook until pasta is al dente, 8 to 10 minutes.
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17
Drain the past and add it to the saute pan along with half of the goat cheese, and toss to combine.
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18
Transfer pasta mixture to a serving dish, and garnish with remaining goat cheese and basil leaves.
