Place first 5 ingredients together in a saucepan and cover with water. Bring to the boil and simmer for 45–50 minutes until chicken is tender and cooked through. Remove chicken from pot and cool. Remove skin and bones, and shred chicken meat.
Melt butter in a saucepan, add flour and stir to form a smooth paste. Gradually add milk, stirring to cook until thickened and smooth. Stir in shredded chicken pieces. Heat oil in a frying pan. Fry leeks and mushrooms until soft and lightly browned. Add to chicken mixture and season with parsley, salt and pepper.
Pour chicken mixture into an ovenproof dish and allow to cool slightly.
Preheat oven to 200°C. Roll puff pastry out on a lightly floured surface. Cover chicken pie filling with pastry and make a hole in the centre for steam to escape. Decorate pastry with pastry leaves or lattice, whatever you fancy, and brush lightly with a little beaten egg. Bake for 25–35 minutes until puffed, golden and crisp.
Serve with a chilled Grolsch.