One-Skillet Chicken Pot Pie

Chicken and Vegetables1 teaspoon vegetable oil 1 whole chicken (about 4 1/2 pounds), cut into 4 pieces (2 breast pieces, 2 leg quarters, wings discarded) and trimmed of excess fat 24 frozen pearl onions, thawed, drained and patted dry (about 1 cup, or 5 ounces) 1 medium onion, cut into 1/2-inch pieces (about 1 cup)4 medium carrots, cut into 1/2-inch pieces (about 1 1/2 cups)3 medium ribs celery, cut into 1/2-inch pieces (about 1 cup) Table salt and ground black pepperSauce4 1/4 cups low-sodium chicken broth4 tablespoons unsalted butter 1/2 cup unbleached all-purpose flour 3/4 cup heavy cream 3/4 cup frozen peas (unthawed, about 3 1/2 ounces)2 teaspoons juice from 1 lemon1 tablespoon minced fresh parsley leaves1 teaspoon minced fresh thyme leavesTable salt and ground black pepperRefrigerated pie dough or All-Butter Pie Dough, recipe BELOWTo roast chicken and vegetables: Adjust oven racks to lower-middle and upper-middle positions; heat oven to 450 degrees. Heat oil in heavy-bottomed 12-inch ovenproof skillet over medium-high heat until oil just begins to smoke; swirl skillet to coat evenly with oil. Brown chicken pieces skin side down until deep golden, 3 to 4 minutes; turn chicken pieces and brown until golden on second side, 3 to 4 minutes longer. Transfer chicken to large plate; drain all but 1 tablespoon fat.Set skillet over medium heat. Add pearl onions and cook, stirring occasionally, until browned, about 3 minutes. Increase heat to medium-high and add onion, carrots, celery, and salt and pepper to taste; cook, stirring occasionally, until vegetables begin to brown, 2 to 3 minutes. Return chicken pieces to skillet skin side up and place in oven on lower-middle rack. Roast until thickest part of breast registers about 160 degrees on instant-read thermometer and thickest part of thigh and drumstick registers about 175 degrees, 18 to 25 minutes. Using potholder or oven mitt, remove skillet from oven. Transfer chicken to platter and let rest 1 hour. Set skillet with vegetables aside. For the sauce and assembling pie: While chicken rests, return skillet with vegetables to medium-high heat. Add chicken broth and any juices from chicken platter and bring to simmer, scraping sides and bottom of skillet with wooden spoon to loosen any browned bits. Pour contents of skillet through medium-mesh strainer set over large bowl; transfer vegetables from strainer to separate bowl and refrigerate. After fat rises to surface of broth, 15 to 20 minutes, skim with ladle or large spoon and discard. (You should have about 3 1/2 cups broth.)When chicken has rested, remove and discard skin. Using fingers or fork, pull chicken off bones into 2-inch shreds and 1-inch chunks; refrigerate until ready to use (you should have about 4 1/2 cups chicken).Wipe skillet clean; melt butter over medium-high heat until foaming. Stir in flour and cook, stirring constantly, until mixture darkens slightly and becomes fragrant, about 1 minute. Slowly whisk in broth and cream and bring to boil; reduce heat to medium and simmer, stirring constantly, until sauce is thickened and coats back of spoon, 8 to 10 minutes. Off heat, add chicken, reserved vegetables, peas, lemon juice, parsley, thyme, and salt and pepper to taste; gently stir to combine.Remove dough from freezer, lift off parchment paper, and place dough on top of filling. Bake on upper-middle rack at 450 degrees until crust begins to brown around edges, about 15 minutes; reduce heat to 375 degrees and continue to bake until crust is golden brown and filling bubbles, 15 to 20 minutes more. Let cool 15 minutes before serving. Serves six to eight.Cook's note: Substitute 3-3 1/2 pounds of bone-in, skin-on chicken parts for the whole chicken, if desired. The chicken and vegetables can also be prepared the day before.Nutrition values per serving: 394 calories, 23 g fat (11 g saturated), 18 g carbohydrates, 3 g fiber, 28 g protein, 122 mg cholesterol, 1,047 mg sodium.Cook's Illustrated, February 2006