Modified from marthastewart.com.
This recipe yields three medium-sized or two large potpies. You can make ahead and freeze. To save time, you can also make the dough ahead and refrigerate overnight a day or so until you are ready to make the stew.
3 lbs. boneless skinless chicken breast
6 cups chicken broth (one large 49.5 oz. can will do)
1 large yellow onion
3 dried bay leaves, broken in half
1/2 teaspoon whole black peppercorns
1 small bunch fresh thyme
1 rib celery, cut into thirds
2 1/2 cups flour
1 tablespoon salt
2 1/2 sticks butter
2 large egg yolks
3 lbs. yukon gold potatoes, scrubbed and cut into 1/2-inch pieces
1 medium leek, sliced into 1/4-inch-thick rounds and washed
3 medium carrots, sliced into 1/4-inch-thick rounds
1 15 oz. can green beans, drained
1 15 oz. can corn, drained
1 1/2 cup milk
Zest of 1 lemon
1 tablespoon freshly ground black pepper
Combine chicken, chicken stock, yellow onion (hack it up into four pieces, no need to peel), bay leaves, peppercorns, 3 thyme sprigs, and celery in a stockpot, and add enough water just to cover the chicken. Bring stock to a boil, reduce heat, and simmer, uncovered, for 1 hour, so stock reduces.
Pick enough thyme leaves to make 3 tablespoons. Combine 2 cups flour, 1/2 teaspoon salt, and 2 tablespoon thyme leaves in the bowl of a food processor, and set remaining one tablespoon thyme aside. Add 2 1/2 sticks chilled butter and pulse until mixture resembles coarse meal. While the food processor is running, add 2 egg yolks and enough ice water until the dough is holding together (kind of flopping around in the food processor). Turn dough onto plastic wrap, flatten into circle, and wrap well; refrigerate at least 1 hour.
Drain chicken, and reserve the stock. Shred the chicken into bite-size strips, and set aside. Strain the stock and set aside.
Preheat oven to 375. Saute red potatoes in canola oil until the potatoes begin to turn golden, about 7 minutes. Add leeks and carrots and cook 4 to 5 minutes more. Add 1/2 cup flour and cook, stirring, for 1 minute. Stir in reserved chicken stock and milk, and bring to a simmer. Cook until thick and bubbly, stirring constantly, 2 to 3 minutes. Add reserved chicken pieces, remaining tablespoon thyme, lemon zest, 1 tablespoon salt, and the ground pepper; transfer to two or three large casserole dishes (depending on how many pies you are making). Set aside.
Divide dough, one piece per pie. Roll out the dough until it is 1/4 inch thick, and transfer to a baking sheet. Allow to chill 15 minutes. Place the dough over the top of the chicken mixture, and tuck extra dough around the edges. Cut slits on top to allow steam to escape. Place pie(s) on a baking sheet. Bake until crust is golden, 35 to 40 minutes. Serve hot.
If refrigerated overnight, bake one hour at 375.