Heat olive oil in a large skillet over medium heat. Add garlic, onion, carrots, oregano, thyme, salt, and pepper. Cook until vegetables are tender, about 5 minutes.
Stir in flour and cook for 1 minute. Gradually stir in chicken broth and bring to a boil. Reduce heat and simmer until thickened, about 5 minutes.
Stir in chicken, peas, and butter. Divide filling into two 9-inch pie crusts.
In a small bowl, stir together 1/4 cup flour and milk until smooth. Pour over chicken mixture.
Cover with top crust, seal edges, and cut away excess dough. Make several small slits in the top to allow steam to escape.
Bake in preheated oven for 30 minutes, or until crust is golden brown.
Interesting Facts
Chicken pot pie is believed to have originated in the United Kingdom.
The first printed recipe for chicken pot pie was in the 18th century.
The dish has been a comfort food in the United States since the 19th century.