Ingredients
1 stick unsalted butter
1 1/4 cups unbleached all-purpose flour, plus more for dusting
1/2 teaspoon kosher salt
1 whole chicken (3 1/2 pounds), quartered
2 leeks, white and pale-green parts thinly sliced (2 cups), 6 dark-green tops reserved
3 stalks celery, 1 halved, 2 chopped (3/4 cup)
8 ounces cremini mushrooms, stems removed and reserved, caps coarsely chopped
1/2 small butternut squash, seeded, peeled, and chopped (2 1/2 cups), peelings reserved
Kosher salt and freshly ground pepper
4 cups low-sodium chicken broth
6 tablespoons unsalted butter
1/3 cup unbleached all-purpose flour
1 tablespoon fresh thyme leaves
1/2 cup dry white wine, such as Sauvignon Blanc
1 cup frozen peas, thawed
1/2 cup packed chopped fresh flat-leaf parsley leaves
1 large egg white
Preparation
Crust:Melt butter in a medium saucepan over medium-high. When it boils, reduce heat to medium; simmer until foamy. Continue cooking, stirring occasionally and scraping bottom of pan, until foam subsides, butter turns golden brown with a nutty aroma, and milk solids separate into brown specks that sink to bottom, 2 to 7 minutes. Remove from heat; immediately transfer to a heatproof bowl. Let cool completely. Pour into an ice-cube tray, filling cups halfway. Freeze until cold and firm, about 1 hour. Pulse flour and salt in a food processor to combine. Add chilled brown butter; pulse until mixture resembles coarse meal with some pea-size lumps. Drizzle with 3 tablespoons ice water. Pulse until mixture just begins to hold together. (If mixture crumbles when squeezed in your hand, drizzle with 1 more tablespoon ice water and pulse a few more times.) Transfer to a piece of plastic wrap; knead just until dough holds together. Loosely cover and shape into a disk. Wrap tightly and refrigerate until firm, about 1 hour.
Filling:Meanwhile, combine chicken, reserved leek tops, halved celery, mushroom stems, squash peelings, and 1 tablespoon salt in a large pot. Add broth and enough water tojust cover chicken. Bring to a boil, then reduce heat to medium and simmer until a thermometer inserted into thickest parts of chicken (without touching bones) registers 160 degrees, about 20 minutes. Transfer chicken to a plate. Strain broth; reserve 2 1/2 cups (refrigerate or freeze remainder for another use).
Brown butter for filling in pot. Add sliced leeks and chopped celery, mushroom caps, and squash; season with salt and pepper. Cook, stirring occasionally, until squash begins to soften, about 5 minutes. Stir in flour and thyme; cook until darkened slightly and nutty, about 2 minutes. Add wine; boil until mostly evaporated, about 30 seconds. Stir in reserved broth and bring to a boil, then remove from heat. Pull chicken from skin and bones and tear into bite-size pieces. Stir into pot with peas and parsley. Transfer to a 3-quart baking dish. (Filling can be made up to 2 days ahead and refrigerated; stir in peas and parsley just before baking.)
Preheat oven to 400 degrees. On a floured work surface, roll out dough to a diameter slightly larger than baking dish. Center dough over filling; trim edges to a 1/2-inch overhang. Beat egg white with 1 teaspoon water; brush over dough. Cut vents in center. Bake until crust is golden brown and filling bubbles, 35 to 45 minutes. Let cool 20 minutes before serving.
Melt butter in a medium saucepan over medium-high. When it boils, reduce heat to medium; simmer until foamy. Continue cooking, stirring occasionally and scraping bottom of pan, until foam subsides, butter turns golden brown with a nutty aroma, and milk solids separate into brown specks that sink to bottom, 2 to 7 minutes. Remove from heat; immediately transfer to a heatproof bowl. Let cool completely. Pour into an ice-cube tray, filling cups halfway. Freeze until cold and firm, about 1 hour. Pulse flour and salt in a food processor to combine. Add chilled brown butter; pulse until mixture resembles coarse meal with some pea-size lumps. Drizzle with 3 tablespoons ice water. Pulse until mixture just begins to hold together. (If mixture crumbles when squeezed in your hand, drizzle with 1 more tablespoon ice water and pulse a few more times.) Transfer to a piece of plastic wrap; knead just until dough holds together. Loosely cover and shape into a disk. Wrap tightly and refrigerate until firm, about 1 hour. Meanwhile, combine chicken, reserved leek tops, halved celery, mushroom stems, squash peelings, and 1 tablespoon salt in a large pot. Add broth and enough water tojust cover chicken. Bring to a boil, then reduce heat to medium and simmer until a thermometer inserted into thickest parts of chicken (without touching bones) registers 160 degrees, about 20 minutes. Transfer chicken to a plate. Strain broth; reserve 2 1/2 cups (refrigerate or freeze remainder for another use).
