In a saucepan, combine chicken, carrots, peas and celery. Add water barely to cover (not too much) and boil for 15 minutes. Remove from heat, drain and set aside.
In the saucepan over medium heat, cook onions in butter until soft and translucent. Stir in flour, salt, pepper and celery seed. Slowly stir in chicken stock and milk. Simmer over medium-low heat until thick. Remove from heat and set aside.
Place one of the puff pastry sheets into 23cm pie dish and press it in. Pour hot liquid mixture over. Cover with the top piece of pastry, seal edges and cut away excess dough. Make several small slits in the top to allow steam to escape and crimp the edges and brush with milk if desired.
Bake in the preheated oven for 30 to 35 minutes or until pastry is golden brown and filling is bubbly. Cool for 10 minutes before serving.