01 - Preheat oven to 400°F.
02 - Melt butter in a large skillet over medium heat. Add onions, carrots, and celery; sauté for 5 minutes until softened.
03 - Stir in flour and cook, stirring constantly, for 1 minute.
04 - Gradually whisk in chicken broth and milk. Simmer until thickened, about 3 to 4 minutes.
05 - Add salt, pepper, thyme, and garlic powder. Stir in cooked chicken, peas, and corn. Simmer 2 minutes then remove from heat.
06 - Pour filling into a 9x13-inch casserole dish.
07 - Unroll puff pastry over filling, trimming excess. Cut small slits to allow venting.
08 - Brush puff pastry with beaten egg to achieve golden crust.
09 - Bake for 30 to 35 minutes until crust is golden brown and filling bubbles.
10 - Let rest for 10 minutes before serving.