Old-Fashioned Chicken Pot Pie

1. FOR THE PIE DOUGH: Process flour and salt in food processor until combined. Scatter shortening over top and pulse until mixture resembles coarse cornmeal, about 10 pulses. Scatter butter pieces over top and pulse mixture until it resembles coarse crumbs, about 10 pulses; transfer to large bowl.
2. Sprinkle 3 tablespoons ice water over flour mixture. Stir and press dough together, using stiff rubber spatula, until dough sticks together. If dough does not come together, stir in remaining 1 tablespoon water.
3. Turn dough onto sheet of plastic wrap and flatten into 4-inch disk. Wrap dough tightly in plastic and refrigerate for at least 1 hour. Before rolling out dough, let it sit on counter to soften slightly, about 10 minutes.
4. FOR THE FILLING: Bring chicken and broth to simmer in covered Dutch oven and cook until chicken is tender and cooked through, 8 to 10 minutes. Transfer chicken to large bowl. Pour broth through fine-mesh strainer into liquid measuring cup and reserve. Do not wash pot. Meanwhile, adjust oven rack to lower-middle position and heat oven to 400 degrees.
5. Heat oil in now-empty pot over medium heat until shimmering. Add onion, carrots, celery, 1⁄4 teaspoon salt, and 1⁄4 teaspoon pepper and cook until softened, about 5 minutes. While vegetables are cooking, use 2 forks to shred chicken into bite-size pieces. Transfer vegetables to bowl with chicken; set aside.
6. Melt butter in again-empty pot over medium heat. Add flour and cook, stirring constantly, for 1 minute. Slowly whisk in reserved chicken broth, milk, any accumulated chicken juices, and thyme. Bring to simmer and cook until sauce thickens, about 1 minute. Off heat, stir in chicken-vegetable mixture, peas, sherry, and parsley and season with salt and pepper to taste.
7. Pour chicken mixture into 13 by 9-inch baking dish. Roll dough out to 15 by 11-inch rectangle, about 1⁄8 inch thick, on lightly floured counter. Loosely roll dough around rolling pin and gently unroll it over filling. Trim, fold, and crimp edges, and cut 4 vent holes in top.
8. Place pot pie on aluminum foil–lined rimmed baking sheet and bake until filling is bubbling on sides and crust is golden brown, about 30 minutes. Let cool for 10 minutes before serving.
   TO MAKE AHEAD: Dough can be wrapped and refrigerated for up to 2 days or frozen for up to 1 month. If frozen, let dough thaw completely in refrigerator before rolling out. Chicken filling can be cooled and refrigerated overnight. Reheat filling before transferring to baking dish and proceeding with recipe.

ARRANGING DOUGH ON A POT PIE
1. After rolling out crust, loosely roll it around rolling pin, then gently unroll it over filled baking dish.
2. Using scissors, trim all but 1⁄2 inch of dough overhanging edge of baking dish. Tuck edges of dough underneath, then crimp using tines of fork.