1 (3 1/2 lb.) frying chicken
1 celery stalk
1 small onion, halved
2 tsp. salt
2 1/4 cups all-purpose flour
3/4 tsp. salt
3/4 cup cold unsalted butter, diced
1/4 cup + 2 T. vegetable shortening, chilled
4 1/2 to 6 T. ice water
6 T. unsalted butter
1 large onion, diced (about 1 1/4 cups)
3 carrots, thinly sliced on the diagonal
3 celery stalks, thinly sliced on the diagonal
1/2 cup all-purpose flour
1 1/2 cups milk
1 tsp. chopped fresh thyme leaves
1/4 cup dry sherry
3/4 cup frozen green peas, thawed
2 T. minced fresh parsley
2 tsp. salt
1/2 tsp. freshly ground black pepper
1 egg whisked with 1 T. water
Combine chicken and vegetables in large stockpot. Add cold water to cover and bring to boil; reduce heat and simmer for 45 minutes. Transfer chicken to plate and allow to cool. Boil broth for an additional 20 minutes. Strain, and discard vegetables, saving broth. Shred cooled chicken into bite-size pieces.
To prepare dough, combine flour, salt and butter in the bowl of a food processor and pulse 5 times. Add the shortening and pulse a few more times, until the dough resembles coarse cornmeal. Add ice water 1 T. at a time, pulsing a couple of times after each addition. Add only enough water to form the dough into a ball. Remove the dough and flatten into a disk. Wrap with plastic wrap and refrigerate for at least 30 minutes before rolling.
Preheat the oven to 400 degrees. Place a large saucepan over medium heat and add the butter. When the butter is melted, add the onion, carrots, and celery and cook, stirring occasionally, for 10 minutes, until the onion is soft and translucent. Add the flour and cook, stirring, for 1 minute. Slowly whisk in the milk and 2 1/2 cups of chicken broth. Decrease the heat to low and simmer, stirring often, for 10 minutes. Add the chicken meat, thyme, sherry, peas, parsley, salt and pepper and stir well. Taste and adjust the seasoning as necessary. Divide the warm filling among six individual ramekins.
Place the dough on a floured surface and roll out to 1/4 inch thick. Cut into six rounds for ramekins about 1" larger around than ramekin. Tuck the overhanging dough under itself and flute the edges with a fork. Cut a 1-inch slit in the top of each pie. Brush the tops of the pies with the egg wash. Line a baking sheet with aluminum foil. Place the pies on the baking sheet and bake for 25 minutes until the pastry is golden and the filling is bubbling.