Step 1

Place chicken in a medium Dutch oven or large saucepan, skin-sides down. Cover with broth and 2 cups water; add 1 teaspoon salt. Bring to a boil, then reduce heat to low and simmer, uncovered, until chicken is just cooked through, about 20 minutes. Transfer chicken to a plate; let cool about 30 minutes. Strain broth, discarding solids (you should have about 3 1/2 cups).

Step 2

Remove chicken from bones and shred meat into bite-size chunks. Discard skin and bones. You'll need 2 1/2 cups chicken; save the rest for salads or sandwiches.

Step 3

Wash and dry Dutch oven or saucepan; add bacon and cook over medium heat until crisp, 7 to 9 minutes. Remove bacon with a slotted spoon and transfer to a paper-towel-lined plate. Discard all but 1 tablespoon fat from Dutch oven.

Step 4

Add mushrooms to pot and cook over high heat until golden brown and liquid has evaporated, about 6 minutes. Add butter, leeks, carrots, celery, potato, 1 teaspoon salt, and some pepper. Cook, stirring, until leeks are translucent, about 4 minutes. Add wine; cook until mostly evaporated, about 1 1/2 minutes.

Step 5

Stir in flour; cook 20 seconds, stirring constantly. Stir in 2 3/4 cups broth. Bring to a boil, then reduce heat and simmer, stirring often, until potato is just barely tender, about 5 minutes (mixture will look very thick; that's okay, as the vegetables will release liquid in the oven).

Step 6

Stir in chicken, peas, reserved bacon, and thyme. Season to taste; divide filling into to four small baking dishes or ramekins (with about 2 cups capacity), and let cool 30 minutes, or refrigerate, covered, up to 1 day. (See cook's note for baking dish dimensions for one large potpie.)

Step 7

Preheat oven to 375°F. Roll each disk of Pâte Brisée out 1/8 inch thick; cut out rounds just larger than the diameter of individual baking dishes. Drape rounds over dishes with cooled filling; cut 5 vents in each crust and brush with beaten egg. Transfer dishes to a rimmed baking sheet and bake until golden brown and bubbling in center, 45 to 50 minutes. Let cool 20 minutes before serving.