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1
Preheat the oven to 400F.
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2
Lightly grease an ovenproof 9- or 10-inch skillet or a 2-quart baking or souffle dish.
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3
Toss the squash in a bowl with the olive oil to lightly coat.
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4
Season with salt and pepper to taste, spread evenly on a rimmed baking sheet, and bake until tender and golden brown, 25 to 30 minutes.
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5
Remove from the oven and set aside.
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6
Melt the butter in a large skillet over medium-high heat and cook the mushrooms and shallots, stirring frequently, for 5 to 6 minutes, until light brown, adding more butter if needed.
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7
Add the flour and cook, stirring constantly, until light brown, 3 to 4 minutes longer.
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8
Slowly stir in the broth, scraping the brown bits from the bottom of the pan, and bring to a low boil, stirring constantly, until slightly thick, about 5 minutes.
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9
Add the chicken and sage, season with salt and pepper to taste, and stir to mix.
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10
Reduce the heat to a simmer and cook, stirring frequently, until the mixture is thick and creamy, about 10 minutes.
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11
Remove from the heat, stir in the reserved squash, and allow to cool.
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12
Meanwhile, roll the puff pastry on a lightly floured surface just to even out the lines.
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13
Cut the pastry to fit the top of the baking dish, leaving enough excess to allow the pastry to drape over the sides by about 1/4 inch.
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14
Fill the prepared skillet or baking dish with the chicken mixture, leaving about 1/2 inch of space at the top, and place the pastry over the dish.
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15
Cut several slits in the crust to allow steam to escape.
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16
Decorate as desired, brush with the egg wash, and refrigerate for at least 1 hour.
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17
Preheat the oven to 375F.
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18
Place the pie on a rimmed baking sheet and bake until the filling is bubbling around the edges and the pastry is puffy and golden brown, 45 to 50 minutes.
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19
Remove from the oven and serve warm.
