Bring the pastry to room temperature as directed on the package.
Meanwhile, preheat the oven to 375°F (190°C or 180°C for a fan oven).
Place a baking sheet in the oven to preheat as well.
Melt the butter in a large frying pan over medium heat.
Sauté the onion for about five minutes or until it just begins to soften.
Sprinkle the flour over top of the onion and cook for a minute or two.
Gradually add the beef stock, stirring after each addition until the mixture begins to thicken.
Add half a cup of the milk in the same way.
Stir in the shredded roast beef and vegetables.
Add enough of the remaining milk to make a thick, creamy filling.
Season with salt and pepper, tasting as you go.
Remove the filling mixture from the heat.
Carefully unroll one of the pastry sheets over a medium pie dish, ensuring the paper is uppermost so that it can be removed once the pastry is in the pie dish. Remove the paper.
Gently press the pastry into the tin and around the rim.
Prick the pastry several times with a fork.
Brush the rim of the pastry with the beaten egg.
Spoon the beef and vegetable mixture into the pie dish.
Unroll the second piece of pastry over the filling, ensuring the paper is uppermost. Remove the paper.
Press the edges of the pie on the rim together to seal.
Use a sharp knife to trim the pastry around the edge of the tin.
Make a slit in the top of the pie with a knife for steam to escape.
Use your fingers to crimp the edge of the pie or press the edges together with a fork.
Brush the top of the pie with beaten egg.
Place the pie dish on the preheated baking sheet.
Bake for 20 to 25 minutes or until the pastry is crisp and golden.