Better Chicken Pot Pies

1 MAKE PASTRY LIDS: In a large, wide bowl (preferably one that you can get your hands into), combine the flour and salt. Add the butter and, using a pastry blender or your fingertips, cut them up and into the flour mixture until it resembles little pebbles. Keep breaking up the bits of butter until the texture is closer to uncooked couscous.
2 In a small dish, whisk together the sour cream, vinegar, and water, and combine it with the butter-flour mixture. Using a flexible spatula, stir the wet and the dry together until a craggy dough forms. If needed, get your hands into the bowl to knead it a few times into one big ball. Pat it into a flattish ball, wrap it in plastic wrap, and chill it in the fridge for 1 hour or up to 2 days. Meanwhileâ€¦
3 MAKE FILLING: Generously season all sides of the chicken parts with salt and freshly ground black pepper. If your chicken breasts are particularly large, I find that halving them can ensure they cook at the same pace at the other parts. Heat first glug of olive oil over medium-high heat in the bottom of a large Dutch oven (minimum of 4 quarts; mine is 5). Brown chicken in two parts, cooking until golden on both sides. Transfer to a plate and repeat with second half of chicken. Set aside.
4 Heat second glug of olive oil in the same pot. Add onions and leeks, season with salt and pepper, and saute them until softened, about 7 minutes. If using, pour in sherry and use it to scrape up any bits stuck to the bottom of the pan. Simmer until mostly cooked off.
5 Add milk or cream, chicken broth, thyme and bay leaf and bring to a simmer. Nestle the browned chicken and any accumulated juices into the pot. Cover and gently simmer to 30 minutes, after which the chicken should be fully cooked and tender.
6 Transfer the chicken to a cutting board to cool slightly. Discard the bay leaves. Allow the sauce to settle for a few minutes, then skim the fat from the surface using a wide spoon; reserve it for another use or substitute for butter in the next step.
7 In a medium bowl, mash butter (feel free to replace any part of it with skimmed chicken fat from the previous step) and flour together with a fork until a paste forms and no flour is still visibly dry. Pour one ladleful of filling over it, and whisk until smooth. Add a second ladleful, whisking again. Return this butter-flour-filling mixture to the larger pot, stir to combine, and bring mixture back to a simmer for 10 minutes. The brothy base should thicken to a gravy-like consistency. Adjust seasonings, if needed.
8 Add carrots and peas to stew and simmer for 3 minutes, until firm-tender. Shred or dice the chicken, discarding the bones and skin or saving it for another use. Return chicken to stew and re-simmer for 1 minute. Stir in parsley.
9 ASSEMBLE AND BAKE PIES: Heat your oven to 375 degrees F.
10 Divide chilled dough into quarters. Roll each quarter out into rounds that will cover 4 2-cup ovenproof bowls or baking dishes with a 1-inch overhang. Cut vents into rounds.
11 Ladle filling into four bowls, filling only to 1 to 1 1/2 inches below the rim to leave room for simmering. Whisk egg with water to make an egg wash. Brush edges of bowls with egg wash, or if you like lids that easily lift off your bowls and are willing to risk that they may slip slightly into the bowl when baking, you can skip this. Place a lid over each bowl, pressing gently to adhere it to the outer sides of the bowl. Brush the lids with egg wash.
12 Bake until crust is bronzed and filling is bubbling, 30 to 35 minutes.
13 DO AHEAD: The dough for the lids can be made up to 3 days in advance and chilled. The filling can be made up to a day in advance and re-warmed before assembling and baking the pot pies.