Heat the oil in a frying pan, add the chicken and fry until the chicken begins to turn white.
Add the mushrooms and continue to fry until the chicken is golden-brown.
Remove the chicken and mushrooms from the pan and set aside. Add the onion and garlic to the same pan and fry for 2-3 minutes or until softened. Remove from the heat and set aside with the chicken and mushrooms.
Melt the butter in a saucepan, stir in the flour and cook for about three minutes, stirring constantly until it has formed a thick smooth paste (this is called a roux).
Mix the milk and stock together in a jug, then add the nutmeg, white pepper and salt, to taste. Pour the liquid slowly into the flour mixture, whisking all the time until smooth. Simmer over a gentle heat, stirring constantly, for about five minutes or until the sauce has thickened.
Stir in the chopped parsley and pour the sauce over the chicken and mushroom mixture. Mix well, then spoon into a pie dish and leave until completely cool.
Roll out the pastry on a lightly floured surface until it is the thickness of a pound coin. Brush the edges of the pie dish with beaten egg, lay the pastry on top, press down the edges and trim. Brush the top of the pie with beaten egg and cut some leaf shapes out of the left-over pastry to decorate the top of the pie.
Make two or three slits in the top of the pie to allow steam to escape and then bake in the oven for 20-25 minutes or until golden-brown on top.