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