Preheat the oven to 400°F (200°C).
In a medium skillet, heat olive oil and butter over medium heat.
Add the chopped white onion and diced carrots; sauté for about 5 minutes until softened.
Stir in the shredded chicken, frozen peas, cream of chicken soup, chicken broth, and dried thyme.
Simmer the mixture for 5–7 minutes, stirring occasionally, until thickened and heated through. Season with salt and black pepper to taste.
Transfer the chicken and vegetable filling to a pie dish.
Unroll the pie crust and cover the filling, trimming any excess dough and crimping the edges to seal.
Cut a few small slits in the crust to allow steam to escape.
Bake the pot pie for 25–30 minutes or until the crust is golden brown and crispy.
Let the pot pie rest for a few minutes before serving. Enjoy your warm, homey meal!