01 - Set oven temperature to 400°F.
02 - Melt butter in a large skillet over medium heat. Add onions, carrots, and celery; sauté until softened, about 5 minutes.
03 - Stir in flour and cook, stirring constantly, for 1 minute.
04 - Gradually whisk in chicken broth and milk. Bring to a simmer and cook until thickened, about 3 to 4 minutes.
05 - Season with salt, pepper, thyme, and garlic powder. Stir in cooked chicken, peas, and corn. Simmer for 2 minutes, then remove from heat.
06 - Transfer mixture into a 9x13-inch casserole dish.
07 - Unroll puff pastry over filling, trimming edges as needed. Cut small slits to allow steam to escape.
08 - Brush the puff pastry surface with beaten egg for golden finish.
09 - Place in oven and bake 30 to 35 minutes until crust is golden and filling bubbles.
10 - Remove from oven and allow to cool 10 minutes before serving.