Preheat the oven to 220C/Gas mark 7. Heat the oil in a frying pan and brown the turkey.
Add the leeks, mushrooms and thyme leaves and fry for about 10 mins until softened and slightly caramelised.
Meanwhile make a white sauce: melt the butter in a small saucepan and add the flour, stirring well with a wooden spoon to make a paste. Cook for 1 min. Pour over the milk a little at a time, whisking continually until you have a thick sauce. Crumble in the stock cube and season with pepper to taste.
Mix the turkey mixture with the sauce and pour the filling into a deep pie dish.
Grease the edges of the pie dish with a little butter. Roll out the pastry and transfer to the pie dish to make a lid. Trim the pastry from around the edges and press down to seal.
Brush milk or egg over the pastry to glaze it. Prick it with a fork and place in the oven for 15-20 mins. The pastry should have risen and be golden brown when you take it out.
Allow the pie to stand for 5-10 mins, then serve with steamed vegetables.