Preheat the oven to 400 degrees F and lightly grease a 9-inch pie dish or baking dish.
Melt the butter in a large skillet over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables start to soften.
Sprinkle the flour over the vegetables and stir for 1 minute to form a roux. Slowly pour in the chicken broth while stirring to avoid lumps.
Add the milk, thyme, salt, and pepper. Simmer the mixture for 3 minutes until it thickens into a sauce.
Stir in the diced chicken and frozen peas. Remove the skillet from the heat and pour the filling into the prepared dish.
Lay the puff pastry sheet over the top of the filling. Trim any excess dough and cut a few small slits in the center to let steam escape.
Bake for 25 minutes until the pastry turns deep golden brown and the filling bubbles at the edges.