Preheat the oven to 200°C/390°F/Gas 6.
In a large saucepan, place the whole chicken along with chopped onion, garlic cloves, bay leaves, black peppercorns, thyme, and water. Bring to a boil, then simmer for 1 hour until the chicken is cooked.
Remove the chicken from the pan and let it cool. Reserve the stock.
Shred the chicken meat into small pieces with a fork.
In a separate pan, melt the butter over medium heat. Add chopped leek and carrots, and cook for 5 minutes until soft.
Add plain flour and mix well to create a roux paste. Gradually add 500ml of the reserved chicken stock, stirring constantly.
Stir in double cream and tarragon. Add the shredded chicken and mix well. Season with salt and black pepper to taste.
Roll out the puff pastry to 3 mm thick.
Place the chicken mixture into a pie dish and cover it with the puff pastry.
Brush the edge of the pie dish with egg yolk, then place the pastry over the chicken mixture, crimp the edges, and brush the top with beaten egg.
Bake the pie for 25 to 30 minutes until the pastry is golden brown and the filling is warm.
Serve with mashed potatoes and vegetables.