Preheat the oven to 400F degrees. Prepare a 10-inch skillet.
If using cooked chicken skip the next two steps.
Melt butter in a skillet. season chicken with salt and pepper. Cook on both sides 4-5 minutes each.
Cover and let the chicken rest for 10 minutes. Shred chicken and keep aside.
Melt rest of the butter in the same skillet. Add chopped onion, celery, and carrot. Saute in medium heat for 2 minutes.
Add sliced mushrooms. Saute for 2 minutes. Stir in the minced garlic. Cook for 30 seconds.
Add flour, thyme, and pepper. Mix and cook for 1-2 minutes. Stir in between to prevent the flour from getting stuck at the bottom and burning.
Stir in the stock and milk along with bay leaves in the skillet. Mix to make a smooth mixture and there are no lumps. Let it simmer for 2-3 minutes. The mixture will thicken.
Switch off the flame. Add shredded chicken and green peas.
Roll the pie sheet a bit to even out the surface. Place the lid of the skillet on the sheet as a measurement and cut out a circle a little larger than the lid.
With the help of a rolling pin, shift the pie dough cut out on top of the skillet. Pinch around the edges to create a pattern.
With the help of a knife make a few holes( to help the steam escape)
Brush the pie dough with egg wash. Bake until the crust is golden, about 25 to 30 minutes. Sprinkle the parsley on top (optional) then serve.