Preheat your oven to 425°F (220°C).
In a large skillet, melt the butter over medium heat.
Add the chopped onion, carrots, celery, and cook until soft.
Stir in the flour and cook for 1-2 minutes.
Gradually whisk in the chicken broth, ensuring no lumps remain.
Add the heavy cream, thyme, peas, and shredded chicken.
Season with salt and pepper, adjusting to taste.
Pour the filling into a pie dish and cover with a pie crust.
Cut slits in the top crust to allow steam to escape.
Bake in the preheated oven for 30-35 minutes or until golden.
Let the pie rest for 10 minutes before serving.