- For the crust:
- 2 1/2 cups (12 1/2 ounces) all-purpose flour, divided
- 2 tablespoons granulated sugar
- 1/2 teaspoon salt
- 16 tablespoons (8 ounces) cold unsalted butter, cut into 1/4-inch cubes
- 6 to 7 tablespoons whole milk
- For the filling:
- 2 cups homemade or store-bought low sodium chicken broth
- 1 1/2 pounds skinless, boneless, chicken thighs, legs, breasts, or a mix
- 3 tablespoons olive oil
- 3 medium leeks, white and light green parts, washed, halved vertically and cut into 1/2-inch half moons (about 3 cups)
- 2 medium stalks celery, cut into 1/4-inch pieces (1 cup)
- 2 medium carrots, peeled, halved vertically and cut into 1/2-inch half moons (1 1/3 cups)
- Kosher salt and freshly ground black pepper
- 4 tablespoons unsalted butter
- 1/4 cup all-purpose flour
- 1 cup plus 2 teaspoons whole milk, divided
- 3 tablespoons chopped parsley
- 1 tablespoon finely chopped fresh thyme leaves
- 1 cup frozen peas
- 1 large egg yolk
For the Crust: In food processor, place half the flour, the sugar, and salt, and pulse to combine. Add butter cubes and pulse until mixture resembles wet cornmeal. Add remaining flour and pulse once or twice to combine.
Transfer mixture to large bowl and using rubber spatula, stir in 6 tablespoons milk, pressing mixture against sides of bowl, until mixture comes together into a dough. If too dry, add remaining tablespoon milk. Wrap 1/3 of dough in plastic wrap, pressing into 4-inch disc. Wrap remaining 2/3rds in plastic and pressm into bottom of 10-cup soufflé dish (see note above). Place soufflé dish and dough disk into refrigerator.
For the filling: In large saucepan or Dutch oven, heat chicken broth on medium heat until simmering. Add chicken and simmer until just cooked through, 8 to 10 minutes. Remove from heat and allow chicken to cool in broth. When chicken is cool enough to handle, remove from broth, shred into bite size pieces, and transfer to medium bowl. Strain broth, reserving 3/4 cup and pouring remaining broth over chicken. Set aside.
In same unwashed saucepan, heat oil over medium heat until shimmering. Add leeks, celery, and carrots. Season with salt and pepper. Cook, stirring occasionally, until vegetables are almost soft, 8 to 10 minutes. Add vegetable mixture to chicken.
In same saucepan, heat butter on medium heat until melted. Stir in flour until smooth. Cook, stirring constantly, until raw flour aroma is gone and flour is pale golden blond, about 1 minute. Whisking constantly, slowly add 1 cup milk and 3/4 cup reserved chicken broth, scraping up any bits that have accumulated on the bottom, and cook until mixture is smooth and comes to boil.
Remove from heat and stir in vegetable/chicken mixture, parsley, and thyme. Stir in frozen peas. Season to taste and transfer mixture to large bowl. Cover and chill until just cool, about 1 hour.
Meanwhile, adjust oven rack to lower-middle position and place pizza stone on rack. Preheat oven to 400°F for 45 minutes.
On lightly floured surface, roll out larger piece of dough to 14-inch circle. Roll up dough with rolling pin and then unroll over souffle dish, allowing dough to fit into bottom and completely up the sides. If very soft, chill dough in dish until dough is firm, about 15 minutes.
Fill crust with cooled chicken filling. Roll out remaining piece of dough to 9-inch circle and place over the top. Press the edges together, trim, and crimp with fork.
In small bowl, whisk yolk and remaining 2 teaspoons milk. Brush over top crust. Poke a few slits into the top of the crust. Place a piece of parchment paper on the pizza stone and place the pot pie on top.