Preheat the oven to 425°F (220°C).
In a large skillet, sauté onions, carrots, and celery until softened.
Stir in the flour and cook for 1 minute.
Gradually add chicken broth and milk, stirring constantly until thickened.
Add shredded chicken, peas, thyme, salt, and pepper; mix well.
Remove from heat and let cool slightly.
Roll out the pie crust and place it in a pie dish.
Pour the chicken mixture into the crust.
Cover with a second pie crust, sealing the edges.
Cut slits in the top crust for steam to escape.
Bake for 30-35 minutes until golden brown.
Let it cool for 10 minutes before serving.