- Combine flour and sugar into the bowl of an electric mixer. Cut butter or margarine or butter and shortening into tablespoon pieces; add it to the flour and butter. Use the paddle beater to cut the butter and flour together. Alternatively, this can be done by hand with a pastry blender.
- With the mixer on low speed , or while stirring the mixture with a fork, pour in the cold water. When the dough starts to clump, and before it turns into a ball, stop stirring.
- Lightly knead dough in the bowl until it forms a ball. Divide dough into two parts. Flatten each part into a disk, and chill for about 30 minutes before rolling.
- Preheat oven to 425 degrees F (220 degrees C.)
- In a saucepan, combine chicken, carrots, peas, and celery. Add water to cover 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 broth and milk. Simmer over medium-low heat until thick. Remove from heat and set aside.
- Place the chicken mixture in bottom pie crust. Pour hot liquid mixture over. Cover with top crust, seal edges, and cut away excess dough. Make several small slits in the top to allow steam to escape.
- 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.