PreparationMake dough: 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. 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. 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. (If you overwork dough or add too much water, pastry will be tough.) Turn dough out onto a lightly floured work surface and divide into 6 portions. With floured heel of your hand, smear each portion once in a forward motion to help distribute fat. Form each portion into a disk, rotating on work surface. Wrap disks separately in wax paper or plastic wrap and chill until firm, at least 1 hour and up to 8. Make filling while dough chills: Heat 1 tablespoon oil in a large heavy skillet over moderately high heat until hot but not smoking, then sauté mushrooms, stirring, until browned and dry, about 6 minutes. Transfer to a large bowl. Add remaining 2 tablespoons oil to skillet and cook onion and garlic over moderate heat, stirring, until softened, about 5 minutes. Add onion to mushrooms. Peel potato and cut into 1/2-inch cubes, then add to mushroom mixture with steak, carrots, parsley, salt, and pepper, tossing well. Cool completely. Assemble pasties: Roll out 1 piece of dough on lightly floured surface into a 9-inch round (keep remaining pieces covered). Mound 1 cup filling on round, slightly off center. Brush a 1/2-inch border on dough with water and fold dough over to form a half-moon. Trim edge with a fluted pastry wheel or a knife, then crimp to seal. Cut 3 small steam vents in top crust with a sharp knife and put pasty on 1 of 2 buttered large baking sheets. Make more pasties with remaining dough and filling, then chill 30 minutes, loosely covered. Preheat oven to 350°F. 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. Cool slightly before serving.
PreparationMake dough: 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. 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. 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. (If you overwork dough or add too much water, pastry will be tough.) Turn dough out onto a lightly floured work surface and divide into 6 portions. With floured heel of your hand, smear each portion once in a forward motion to help distribute fat. Form each portion into a disk, rotating on work surface. Wrap disks separately in wax paper or plastic wrap and chill until firm, at least 1 hour and up to 8. Make filling while dough chills: Heat 1 tablespoon oil in a large heavy skillet over moderately high heat until hot but not smoking, then sauté mushrooms, stirring, until browned and dry, about 6 minutes. Transfer to a large bowl. Add remaining 2 tablespoons oil to skillet and cook onion and garlic over moderate heat, stirring, until softened, about 5 minutes. Add onion to mushrooms. Peel potato and cut into 1/2-inch cubes, then add to mushroom mixture with steak, carrots, parsley, salt, and pepper, tossing well. Cool completely. Assemble pasties: Roll out 1 piece of dough on lightly floured surface into a 9-inch round (keep remaining pieces covered). Mound 1 cup filling on round, slightly off center. Brush a 1/2-inch border on dough with water and fold dough over to form a half-moon. Trim edge with a fluted pastry wheel or a knife, then crimp to seal. Cut 3 small steam vents in top crust with a sharp knife and put pasty on 1 of 2 buttered large baking sheets. Make more pasties with remaining dough and filling, then chill 30 minutes, loosely covered. Preheat oven to 350°F. 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. Cool slightly before serving.