Preheat the oven to 220°C (200°C fan oven) Gas Mark 7. Mix together the onion, potato, parsnip, parsley and grated cheese with ½ tsp salt and plenty of black pepper – at least 1 tsp.
Cut the pastry into quarters then, one by one, roll each quarter to a 20cm round (you can use a plate or cake tin bottom to measure and trim). Firmly pack a quarter of the filling mixture along the centre of each round, leaving a border at each end. Brush the pastry all the way around the edge with some egg, then carefully lift up both sides so they meet at the top. Pinch together to seal, then gently lift onto a lightly floured baking tray and brush with the last of the egg to glaze.
Bake the pasties for 10 minutes, then reduce the oven to 180°C (160°C fan oven) Gas Mark 4 and cook for 45 minutes more until golden. Delicious served hot or cold.