In a saucepan, combine chicken, peas, and celery. Add water to cover and boil for 15 minutes. Remove from heat, drain water, add carrots and set aside.
In the saucepan over medium heat, cook onions and garlic 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 stirring constantely. Remove from heat, stir in basil and parsley.
Bake bottom crust in preheated oven 5 minutes.
Place chicken mixture on 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 for 30 to 35 minutes, or until pastry is golden brown and filling is bubbly. Cool for 10 minutes before serving.