For the pastry:
Bring the fat, cream of tartar and the flour together and very briefly rub to breadcrumbs. Add the water and bring together until the mixture has only just become a dough. Mould into a ball and rest for ten minutes.
On a floured surface, take the butter and with your hand or a rolling pin flatten the butter until about 1 1/2 cm thick square. Return to the fridge or freezer until very hard.
With a knife, draw a cross across the dough. push out the corners so the dough resembles a square. Place the butter onto the dough at a 45 degree angle and fold the corners of the dough onto the hardened butter so that the dough completely covers the butter.
Immediately roll, fold and roll again. Place in the fridge for 20 to 30 mins, give rolls and folds and rest again. Do one more roll and fold and then roll out 2/3 of the pastry to fit the pie tin, leaving 1/3 for the lid.
For the filling:
Pre-heat the oven to 180°C/gas mark 6.
Cut each chicken breast into thin strips and place in a dish. Pour over the lemon juice and sprinkle over the zest and thyme. Leave to marinate for 30 minutes.
Heat a large non-stick frying pan, add the rapeseed oil and fry the chicken strips for about 5-6 minutes on either side until they are thoroughly cooked all the way through. Remove and cool.
Now, melt the butter in the frying pan and add the leeks and mushrooms. Cook gently for 10 minutes or until the leeks are tender. Add the creme fraiche and cook for 1 minute. Season with some black pepper. Transfer to a plate and spread the mixture out to allow it to cool quickly.
Drain the anchovies, roughly chop them and place them in a small bowl. Add the mustard and mix well. Season with a little black pepper.
Spread the anchovy and mustard mixture all over the bottom of the pastry.
Put half the chicken fillets on top of the anchovy mixture. Cover with half the leek and mushroom mixture. Spoon the other half of the chicken on top and finish with a final mushroom layer.
Roll out the remaining pastry to fit on the top of the pie. Lay it over the top and then bring the overhang of pastry into the centre to meet it. Crimp and fold the edges over to make it all snug. Brush the pastry with beaten egg. Transfer onto a baking tray and chill for an hour or so or overnight if you want.
Bake the pie for 35-40 minutes or until the pastry is golden brown and the inside is very hot. Use a long knife to test how hot it is - gently pop it into the middle of the pie, leave it in for 15 seconds, pull it out and if the knife is hot, so is the filling! It may take a little longer to cook, to ensure the filling is hot, if the pie has been in the fridge for a while.
If this is the case, cover it with foil after the 35-40 minutes and continue to cook until the filling is hot.
Slice and serve the pie with steamed broccoli, peas and carrots.