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 and view the full Food safety at home video.