01 - Set the oven to 400°F (200°C) conventional, or 180°C fan.
02 - Melt butter in a large skillet over medium heat. Add onion, leeks, carrot, and garlic; cook for 5 to 7 minutes until softened.
03 - Add chicken pieces to the skillet and cook for 5 to 6 minutes until no longer pink.
04 - Stir in flour and cook for 1 minute. Gradually whisk in chicken stock until the mixture is smooth and starts to thicken.
05 - Reduce heat, then stir in cream, mustard, and thyme. Simmer gently for 3 to 4 minutes. Season with salt and black pepper to taste.
06 - Remove from heat and let the filling cool slightly before assembling.
07 - Spoon the filling into a 9-inch (23 cm) pie dish. Unroll puff pastry and cover the dish, trimming excess. Seal edges and cut a small slit in the center to allow steam to escape.
08 - Brush the pastry surface with the beaten egg for a golden finish.
09 - Place in the oven and bake for 30 to 35 minutes until the pastry is golden brown and crisp.
10 - Allow the pie to rest for 5 minutes before serving.