Pre-heat the oven to 180°C/160°C fan/gas mark 4.
Heat the butter and olive oil in a large saucepan until the butter has melted. Add the onion and celery to the pan and fry gently for about 10 minutes when the vegetables start to turn translucent.
Add the leeks, garlic, lemon zest, tarragon, thyme leaves and the bay leaf to the pan. Give everything a good stir then continue to fry gently for 15 minutes or until the leeks are softened.
Add the sweet rice flour and mix well into the leeks until all the flour has been absorbed by the mixture. Stir continually with a wooden spoon letting the flour cook through for a few minutes.
Pour in the vermouth and continue stirring for a couple of minutes until the wine has been absorbed.
Pour 400ml of the stock into the pan. Stir continually until the flour dissolves into the stock and the sauce is thick and bubbling. Turn down to a simmer for 10 minutes.
Add the poached chicken and the crème fraiche and season well with salt and pepper. Bring the mixture to a gentle simmer.
Remove from the heat and pour into a 20cm round deep pie dish
Take the ready-rolled puff pastry and cut a thick strip to place on top of the lip of your pie dish. Then place the rest of the pastry on top, cutting away the excess. Tuck onto the pie filling and pinch to the pastry on the lip of the dish.
Whisk the egg and then brush over the top of the pie.
Place the pie in the middle shelf of the oven and bake for 15-20 minutes until the pastry top is golden brown.