Preheat oven to 350. In a 9 or 10 inch cast iron skillet, melt the butter over medium heat. When the butter is hot, add the onions, carrots, and celery. Saute until the carrots are crisp-tender, about 8 minutes.
In a small bowl combine flour, salt, pepper, and celery seed.
When the vegetables are soft, tilt the skillet to one side so that the butter pools at the bottom. Use a whisk to stir in the flour mixture. Combine until a thick paste forms, then slowly add the chicken broth and the milk. You don't need to keep the skillet tilted for this part, but try to mix together the flour/butter with the liquid as much as you can before stirring in the veggies. Cook the mixture until it thickens, just a couple minutes.
Add the chicken and the peas, then turn off the heat.
Lay the pie crust over the skillet, pinch the edges or just squish them down a bit, and sprinkle the top with a little salt and pepper. Promptly place it in the oven. (You don't want your crust to get soggy.) Bake in the preheated oven for 40-45 minutes, or until the crust is golden brown. Let set for 10 minutes before serving.