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1
Blend together flour, salt, and butter in a bowl with your fingertips or a pastry blender (or pulse in a food processor) until mixture resembles coarse meal with some roughly pea-size lumps.
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2
Beat together yolk and 1/3 cup ice water, then drizzle over flour mixture and gently stir with a fork (or pulse in processor) until incorporated.
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3
Gently squeeze a small handful of dough: If it doesn't hold together, add more ice water, 1/2 tablespoon at a time, stirring (or pulsing) after each addition until just incorporated, continuing to test.
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4
(If you overwork dough or add too much water, pastry will be tough.)
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5
Turn dough out onto a lightly floured work surface and divide into 6 portions.
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6
With floured heel of your hand, smear each portion once in a forward motion to help distribute fat.
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7
Form each portion into a disk, rotating on work surface.
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8
Wrap disks separately in wax paper or plastic wrap and chill until firm, at least 1 hour and up to 8.
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9
Heat 1 tablespoon oil in a large heavy skillet over moderately high heat until hot but not smoking, then saute mushrooms, stirring, until browned and dry, about 6 minutes.
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10
Transfer to a large bowl.
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11
Add remaining 2 tablespoons oil to skillet and cook onion and garlic over moderate heat, stirring, until softened, about 5 minutes.
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12
Add onion to mushrooms.
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13
Peel potato and cut into 1/2-inch cubes, then add to mushroom mixture with steak, carrots, parsley, salt, and pepper, tossing well.
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14
Cool completely.
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15
Roll out 1 piece of dough on lightly floured surface into a 9-inch round (keep remaining pieces covered).
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16
Mound 1 cup filling on round, slightly off center.
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17
Brush a 1/2-inch border on dough with water and fold dough over to form a half-moon.
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18
Trim edge with a fluted pastry wheel or a knife, then crimp to seal.
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19
Cut 3 small steam vents in top crust with a sharp knife and put pasty on 1 of 2 buttered large baking sheets.
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20
Make more pasties with remaining dough and filling, then chill 30 minutes, loosely covered.
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21
Preheat oven to 350F.
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22
Brush pasties with egg and bake in upper and lower thirds of oven, switching position and rotating sheets halfway through baking, until golden, about 40 minutes total.
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23
Cool slightly before serving.
