Preheat your oven to 425°F (220°C).

In a large saucepan, combine the cubed chicken, carrots, peas, and celery. Add water to cover and bring to a boil. Reduce heat and simmer for 15 minutes. Drain and set aside.

In the same saucepan, melt butter over medium heat. Add onion and cook until soft and translucent, about 5 minutes.

Stir in flour, salt, pepper, and celery seed until well combined. Slowly stir in chicken broth and milk, creating a smooth sauce.

Simmer over medium-low heat until thick and bubbly, about 5 minutes. Remove from heat and mix in the drained chicken and vegetables.

Place one pie crust in the bottom of a 9-inch pie plate. Pour the hot filling into the crust.

Cover with the second pie crust, seal the edges, and cut several small slits in the top to allow steam to escape. For an extra golden crust, brush the top with a beaten egg (optional).

Bake for 30-35 minutes, or until the pastry is golden brown and the filling is bubbly. Let cool for 10 minutes before serving.