Pre-heat the oven to 180° C.
Heat the butter until melted in a large saucepan over a medium heat. Whisk in the flour until smooth and cook for 2 minutes, whisking occasionally. Whisk in the milk in a slow, steady stream until you have a thickened sauce.
Add the chicken and all the vegetables to the sauce with some seasoning and simmer for 6-8 minutes until the chicken is cooked through, with no pink showing. Spoon into individual pudding bowls (roughly 4 inches in diameter).
Roll the pastry out on a lightly floured surface to 2cm in thickness. Cut the pastry into 4 inch discs and lay over the tops of the pudding bowls. Crimp the edges using the tines of a fork and make a few cross incisions in the tops to let the steam escape while baking.
Brush with the beaten egg and bake on baking sheets for 20-25 minutes until golden brown. Remove and allow to sit for a few minutes before serving.
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home.