Mix together egg and water, set aside.

In a bowl, combine ¼ cup of butter with the flour (use your hands to create a paste). Set aside.

In another bowl, dissolve the cornstarch in the milk. Set aside.

In a large saucepan, sauté the onion, carrot, and celery in the remaining 2 Tbsp butter. Season with salt and pepper. Add the broth, wine, bay leaf , thyme, and potatoes and bring to a boil. Cover and simmer for about 10 minutes or until the vegetables are just tender.

Add the butter mixture and boil gently, stirring until dissolved. Stir in the milk mixture and bring to a boil. Taste and adjust seasonings. Stir in the chicken and peas and parsley. Remove the bay leaf.

Prepare the pastry, making one or two crusts (1/4" thick) cut to fit baking dish (pie plate, casserole dish, fluted pan) with an extra inch around the edges. If using a bottom crust, chill dough for 15 minutes before adding filling. Spoon in filling, wet dough edges with water, then top with chilled crust. Trim off excess, and crimp edges with fingers or a fork.

Bake at 400°F for 45 minutes or until crust is golden brown, and filling is bubbling (you may want to place dish on a baking sheet in case filling bubbles out). Allow to cool 15 minutes before serving.