Make 2 pie crusts and refrigerate. Get my pie crust recipe below.
Fill a stockpot up halfway with water and put in chicken, peas, and sliced carrots. Bring to a boil and boil about 15 minutes or until chicken is done and carrots are tender. Drain and set aside.
In a medium saucepan add butter, onions, and celery (season with salt and pepper and cook on medium-low for just a few minutes until veggies start to appear translucent.
Whisk in flour, milk, and broth.
Stir in salt, pepper, and thyme.
Bring to a simmer and cook about 10-15 minutes or until it's thick and bubbly.
Cut chicken in chunks, and add chicken, peas, and carrots to the creamy mixture.
Taste and season and take off the heat and set aside.