01 - Preheat the oven to 400°F (200°C, 180°C fan, Gas Mark 6).
02 - Melt butter in a large skillet or saucepan over medium heat. Add onion, leeks, carrot, and garlic; sauté for 5–7 minutes until softened.
03 - Add chicken pieces to the skillet and cook for 5–6 minutes until no longer pink.
04 - Stir in flour and cook for 1 minute. Gradually whisk in chicken stock until smooth and beginning to thicken.
05 - Reduce heat and stir in cream, Dijon mustard, and thyme. Simmer gently for 3–4 minutes. Season with salt and freshly ground black pepper to taste.
06 - Remove from heat and allow the filling to cool slightly before assembling.
07 - Spoon the filling into a 9-inch (23 cm) pie dish. Unroll puff pastry and lay over dish, trimming any excess. Press edges to seal and cut a small slit in the center to release steam.
08 - Brush the surface of the pastry with beaten egg to achieve a golden finish.
09 - Bake the pie for 30–35 minutes until the pastry is golden brown and crisp.
10 - Allow to stand for 5 minutes before serving to set.