Preparation

Make the crust

• Put the flour and salt in a food processor and pulse to blend. Add the butter and pulse until the butter pieces are the size of peas, 10 to 12 pulses. Drizzle 3 Tbs. cold water over the mixture. Pulse until the dough forms moist crumbs that are just beginning to clump together, 8 or 9 pulses more.

  Turn the crumbs onto a large piece of plastic wrap and gather into a pile. With the heel of your hand, gently smear the dough away from you until the crumbs come together (two or three smears should do it). Shape the dough into a 4-inch square, wrap tightly in the plastic, and refrigerate until firm, at least 2 hours.

Make the filling

• Heat 2 Tbs. of the oil in a 7- to 8-quart Dutch oven over medium-high heat until very hot. Generously season the chicken with salt and pepper. Working in two batches, brown the chicken well on both sides, 4 to 5 minutes per side, adding 1 Tbs. oil with the second batch. Transfer the chicken to a cutting board and cut into 3/4- to 1-inch pieces (it’s fine if the chicken isn’t fully cooked; it will finish cooking later). Put the chicken in a large bowl.

  Add 1 Tbs. oil to the pot and heat over medium-high heat until hot. Add the mushrooms. Cook without stirring for 1 minute. Continue cooking, stirring occasionally, until well browned, 3 to 4 minutes. Transfer the mushrooms to the bowl of chicken.

  Reduce the heat to medium and add the remaining 1 Tbs. oil and then the onions and carrots to the pot. Cook, stirring occasionally, until the edges are browned, 8 to 9 minutes. Add the garlic and stir constantly until fragrant, about 30 seconds more. Scrape the vegetables into the bowl of chicken and mushrooms.

  Melt the butter in the same pot over low heat. Add the flour and cook, whisking constantly, until the texture, which will be clumpy at first, loosens and smooths out, about 4 minutes. Slowly whisk in the chicken broth and half-and-half. Bring to a boil over medium-high heat, whisking to scrape up any browned bits from the bottom of the pan. Reduce the heat to low and add the potatoes, chicken, and vegetables (and any accumulated juice), and a generous pinch each of salt and pepper. Partially cover the pot and simmer gently (adjusting the heat as necessary), stirring occasionally, until the potatoes and carrots are just tender, 15 to 18 minutes. Stir in the peas, sherry, parsley, thyme, and mustard. Season to taste with salt and pepper.

Assemble the pot pies

• Distribute the filling evenly among six ovenproof bowls or ramekins that are 2 to 3 inches deep and hold at least 2 cups.

  Let the dough soften slightly at room temperature, about 20 minutes. On a lightly floured surface, roll the dough into a 1/8-inch-thick rectangle. With a round cookie cutter (or using a plate as a guide), cut 6 dough circles that are slightly wider than the inner diameter of the bowls (re-roll the scraps if necessary). Cut one small X in the center of each circle.

  Top each bowl of stew with a dough round. With your fingertips, gently press the dough down into the edge of the stew, so that it flares up the sides of the bowl.

Bake the pies

• Position a rack in the center of the oven and heat the oven to 425°F. Put the pot pies on a foil-lined rimmed baking sheet. Bake until the filling is bubbling and the crust is deep golden-brown, about 45 minutes. Cool on a rack for 20 to 30 minutes before serving.

Make Ahead Tips

The dough for the crust can be refrigerated for up to 2 days or frozen for up to 1 month. If frozen, thaw in the refrigerator overnight or at room temperature for about 1 hour before rolling.

The filling can be prepared through the step of adding the peas and seasonings, cooled and refrigerated for up to 8 hours.

The pot pies can be assembled and refrigerated, covered, for up to 1 day before baking and serving.