Preheat the oven to 400°F (200°C).
Melt butter in a large skillet over medium heat. Add chopped onion and celery, then cook for about 5 minutes until softened.
Season the vegetables with salt, black pepper, and garlic powder. Stir in flour and cook for 1 minute to remove the raw flour taste.
Gradually whisk in chicken broth and heavy cream until the mixture is smooth. Continue cooking until the sauce thickens into a creamy consistency.
Add chopped cooked chicken and frozen mixed vegetables. Stir until everything is evenly combined and heated through.
Transfer the creamy chicken mixture to a sheet pan and spread it into an even layer.
Place puff pastry sheets over the filling, trimming or overlapping the edges as needed. Cut several slits into the pastry to allow steam to escape.
Bake for about 30 minutes, until the puff pastry is golden brown and the filling is bubbling.
Allow the pot pie to cool slightly before serving.