Place the chicken halves, carrots, onion, celery, bouquet garni and lemon rind in a stockpot. Add the water, making sure that the chicken and vegetables are completely covered and adding more water, if necessary. Cover the saucepan with a lid and bring to the boil. Reduce the heat to medium-low and simmer for 1 hour.
Transfer the chicken to a plate and set aside to cool. Strain the stock, discarding the vegetables, and pour the stock back into the stockpot. Boil the stock until it is reduced to 2 cups. Transfer the stock to a heatproof jug and place in the refrigerator to chill overnight.
Meanwhile, remove the chicken meat from the bones and chop roughly. Cover the chicken and place in the refrigerator overnight. The next day, remove and discard any fat from the top of the chicken stock.
Melt 1 tablespoon of the butter in a medium saucepan. Add the leeks and cook for 5 minutes, or until soft. Melt the remaining butter in a medium saucepan until hot and bubbling. Add the flour and stir constantly for 1 minute. Remove from the heat and add the 2 cups of stock and the cream in a slow, steady stream, whisking constantly to avoid the sauce becoming lumpy. Return the saucepan to the heat and cook, stirring constantly on medium-high heat, until the sauce comes to the boil and thickens. Add the leeks, chicken meat, parsley and thyme and season to taste with salt and pepper. Spoon the mixture into a 4-cup pie plate. Cover and place in the refrigerator for 2 hours to chill.
Preheat the oven to 200°C. Roll out the pastry to a 32 cm square. Brush the rim of the pie plate with water. Cut two strips 2 cm wide from the pastry square and place them around the rim of the pie plate. Brush the pastry rim with water and place the remaining pastry over the chicken mixture, pressing the pastry onto the rim of the dish with a fork. Trim off the excess pastry and crimp the edges. Cut a cross in the centre of the pastry and press the fresh thyme sprigs into the hole. Brush the pastry top with beaten egg. Place the pie on a baking tray and bake in the preheated oven for 25–30 minutes, or until the pastry is golden and puffed. Serve immediately.