Preheat the oven to 450. Press the pie crust into the bottom of a deep pie plate. Pinch along the edges. Scatter the shredded chicken into the pie crust. Whisk together the flour, stock and milk and then pour over the chicken. Salt and pepper the chicken according to taste. Cut the butter into small pea size pieces and place around the dish.
Unroll the second pie crust onto the top of the pie. Pinch the edges together to form a seal. Paint the top of the pastry crust with the beaten egg.
Bake at 450 x 20 minutes and then 375 for an hour. Allow to rest for 10 minutes before serving so that the juices will congeal.