Preheat oven to 400°F. Grease a 2-quart casserole dish or deep-dish pie plate (or use a 2-quart oven-safe skillet).
In a bowl, whisk together chicken broth and half-and-half. Set aside.
Melt butter in a large skillet over medium-high heat. Add onion, carrots, and celery. Sauté for 10 minutes, until softened.
Add flour and stir for 1 minute.
Reduce heat to medium. Stir in the broth mixture. Cook, stirring regularly, until thickened (about 5 to 6 minutes). Do not let it boil rapidly.
Stir in salt, pepper, chicken, and frozen peas.
Transfer filling to the prepared baking dish. Top with pie crust, trimming and crimping edges as desired. Cut slits in the top to vent.
Bake for 35 to 40 minutes, or until crust is golden brown.
Let rest 10 to 15 minutes before serving.