Preheat the oven to 400°F
Cook diced chicken or other filling ingredients until done
Sauté onions, carrots, and celery in butter until softened
Stir in flour and cook for 1 minute
Add broth and milk, then cook until thickened
Mix in cooked chicken, peas, corn, salt, pepper, and herbs
Pour the filling into a pie dish or baking dish
Cover with pie crust, puff pastry, or biscuit dough
Cut slits in the top crust to vent steam
Brush the top with egg wash or milk
Bake for 30 to 40 minutes until golden brown
Let cool for 10 to 15 minutes before serving