Add butter and saute onion, celery, carrots, potatoes, and dash of salt and pepper for 10-15 min, until onions are translucent.
If using flour as thickener, add flour and stir into mixture for 1 minute.
If using cornstarch as thickener, add cornstarch to small amount of half-and-half and stir till combined.
Combine half-and-half, broth, and white wine and gradually stir into sauteed veggie mixture.
Cook over medium heat and stir until thickened and bubbly.
Add meat, peas, salt, pepper, thyme, and nutmeg and stir well.
Pour into a 2-quart casserole dish and top with pie crust.
Cut 3 slits to allow steam to escape.
Beat the egg and use a pastry brush to generously apply egg to pie crust top.
Bake for 40-50 minutes or until crust is golden brown and filling is bubbly.
* Can be made ahead and kept in the fridge up to two days before cooking or kept frozen for approximately 30 days. Defrost in fridge before baking. If making ahead, brush egg on pastry before dish goes into the oven.