These savory potpies have the leaves and fronds of whole herbs rolled into the dough that tops them -- the result is as pleasing to the eye as it is to the palate.
Put chicken, stock, large onion, bay leaves, peppercorns, thyme sprigs, and celery in a large (8-quart) pot. Add just enough water to cover the chicken. Cover pot; bring mixture to a boil. Uncover; reduce heat. Simmer 1 hour.
Transfer chicken to a cutting board (reserve stock in pot). Remove skin from chicken; discard. Cut meat from bones; discard bones. Using a fork, shred meat into bite-size pieces; set aside.
Pour stock through a fine sieve into a large bowl; discard solids. Set aside 2 cups stock. (Reserve remaining stock for another use; cooled stock can be frozen in an airtight container up to 4 months.)
Melt butter in a large skillet over medium-high heat. Add potatoes and pearl onions. Cook, stirring occasionally, until potatoes begin to turn golden, about 5 minutes. Add leek, carrots, and mushrooms; cook, stirring occasionally, until softened, about 5 minutes more. Add flour; cook, stirring, 1 minute.
Stir in reserved 2 cups stock and the milk. Bring mixture to a simmer; cook, stirring constantly, until thick and bubbling, 2 to 3 minutes. Stir in chicken, parsley, thyme leaves, zest, salt, and pepper.
Divide chicken mixture among 8 (4-by-2-inch) ramekins, filling them almost to the top. Let cool slightly.
Preheat oven to 375 degrees. Roll out pate brisee on a lightly floured surface to 1/4 inch thick. Arrange mixed herbs on top; roll out dough with a lightly floured pin to 1/8 inch thick, gently pressing herbs.
Using a fluted (or plain) round dough cutter (4 1/2 inches in diameter), cut out 8 rounds from dough. Lightly beat egg with 1 tablespoon water. Brush top edges of ramekins with egg wash. Place a dough round over each ramekin; gently press to seal. Chill in freezer until dough is firm, about 10 minutes.
Brush dough with egg wash. Cut 4 slits in top of each round for steam vents. Bake until crust is golden brown and filling is bubbling, 35 to 40 minutes.