Preheat the oven to 350°F (180°C), or 320°F (160°C) fan. Lightly grease 6 cups of a standard muffin pan.
Roll the pastry on a lightly floured surface into a rectangle approximately 9 ½ × 14 ¼ inches (24 × 36cm). Cut it into 6 equal squares, approximately 4 ¾ inches (12cm) across.
Gently ease a square into each greased cup, leaving the excess pastry overhanging.
Combine the chicken, peas, corn, cream and mustard in a bowl. Taste and season with salt and black pepper.
Divide the filling between the pastry cases. Fold the overhanging pastry over the filling and gently press the edges together. Leave a small opening for steam.
Beat the egg in a small bowl with a fork and brush it over the exposed pastry.
Bake for approximately 35 minutes, until the pastry is golden and cooked through and the center of the filling reaches 165°F (74°C). Allow extra baking time if needed.
Let the pies settle briefly in the pan on a wire rack before carefully removing them. Serve hot with your preferred sides.