Preheat oven to 400°F and have a 9x13-inch baking dish or large oven-safe skillet ready.
In a large skillet over medium heat, melt the butter and whisk in the flour, cooking for 1-2 minutes until it forms a paste.
Gradually whisk in the chicken broth and milk, stirring constantly until the mixture thickens, about 5 minutes.
Stir in the thyme, garlic powder, salt, pepper, cooked chicken, and frozen vegetables, mixing until everything is well combined and heated through.
Pour the chicken mixture into your baking dish, lay the puff pastry over the top, trimming edges as needed, and brush with beaten egg.
Cut a few slits in the pastry to vent steam, then bake for 20-25 minutes until the pastry is golden brown and puffed.
Let cool for 5 minutes before serving.