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1
Preheat the oven to 350 degrees F (175 degrees C). Spread hazelnuts onto a baking sheet.
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2
Toast in the preheated oven until golden brown and fragrant, 10 to 15 minutes. Let cool.
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3
Transfer hazelnuts to a food processor and pulse until finely ground. Add flour and salt; pulse to combine. Add butter pieces 1 at time, pulsing in between until mixture has a coarse, grainy texture. Add egg yolk and pulse once. Pour in iced water 1 tablespoon at a time, pulsing once or twice after each addition, until you can pinch the dough together. Do not over-process.
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4
Turn dough out onto a work surface and form into a ball. Wrap in plastic wrap and refrigerate, at least 30 minutes or up to 1 day.
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5
Melt butter in a large frying pan over medium-high heat. Saute shallot for 1 to 2 minutes. Add mushrooms and saute until tender and liquid has evaporated, 5 to 7 minutes. Remove from heat, season with salt and pepper, and let cool completely.
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6
Preheat the oven to 375 degrees F (190 degrees C). Line a 10-inch tart pan with a removable base with parchment paper.
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7
Remove dough from refrigerator and let sit for a few minutes. Roll out into 12-inch circle on a lightly floured work surface. Carefully place dough into the prepared tart pan. Roll a pin over the top of the dough to trim it. Gently crimp the dough rim along the fluted edge of the pan. Line the tart shell with a piece of aluminum foil and fill with pie weights or dried beans.
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8
Bake in the preheated oven until set to the touch, 8 to 10 minutes. Remove the weights and foil; continue baking until shell is golden, about 5 minutes more. Transfer to a rack to let cool. Reduce oven temperature to 350 degrees F (175 degrees C).
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9
Place chevre cheese in a bowl and lightly beat with a wooden spoon until mostly smooth. Add eggs and beat to combine. Mix in half-and-half until smooth. Season with salt and pepper.
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10
Pour cheese mixture into the pastry shell. Scatter the cooled mushrooms evenly on top, gently pressing them in. Sprinkle parsley on top.
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11
Bake in the preheated oven until pastry edges are browned and filling is set, about 30 minutes. Transfer to a rack and let cool completely, at least 30 minutes.
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12
Remove the pan sides and place tart on a serving plate. Serve at room temperature.
