Preheat oven to 425 degrees. Butter 8" deep dish and set aside.

Heat diced chicken and chicken broth together in small saucepan over medium-high heat. Bring to a boil then remove from heat, cover with lid and set aside.

Melt butter in large skillet over medium-high heat. Add onion, celery, carrots, mushrooms and thyme. Sauté 2 minutes, reduce heat to medium-low and cover. Cook 5−6 minutes with lid on, stirring occasionally (do not allow vegetables to brown). Remove lid, sprinkle vegetables with flour. Stir until flour is completely incorporated and allow to cook 1 minute.

Pour reserved chicken broth and diced chicken into skillet and stir well to dissolve flour into broth. Stir in milk or half-and-half and bring to a boil. Immediately reduce heat to low and simmer 6−8 minutes until thick and creamy. Remove from heat, add peas and season to taste with salt and pepper.

Transfer mixture to pie dish and set aside.

Unfold and roll out puff pastry until just large enough to cover pie dish. Brush small amount of egg along rim of pie dish (this will help pastry adhere to dish). Cover dish with puff pastry and trim excess from edges. Use excess pastry to make decorations for top of pie if desired; adhere decorations using egg wash as glue. Brush entire top crust with egg wash and sprinkle with salt and pepper (optional). Cut several small slits in pastry to vent steam, place pie dish on baking sheet and immediately move pie to oven.

Bake 20−25 minutes until dark golden brown and bubbly. Allow to cool 10 minutes before serving and enjoy!