Prepare the pastry lids first so they can chill. Roll out the pastry thinly on a lightly floured surface and cut out rounds 2.5cm (1in) larger than the dishes you are going to use.
Flour these lightly and put them on a baking-sheet. Roll out the trimmings to make strips about 1cm (½in) wide to fit round the top of each dish. Make leaves out of the rest of the trimmings. Put all these on the baking-sheet and place in the coldest bit of the fridge (or briefly in the freezer). Preheat the oven to 200°C/400°F/gas mark 6 and put a metal baking-sheet into it.
Remove the coarser outside leaves from the leek and trim off the base and the dark green tops (you can use the green bits for soup). Cut the leek into rings about 2cm (¾in) thick. Wash thoroughly in running water and drain. Put these into a saucepan and add the stock. Bring to the boil then turn down to a simmer and cook until tender. Drain off the stock into a measuring jug – you should have about 50ml left – and add enough milk to bring it up to 150ml.
Melt 15g of the butter in a small frying pan and quickly saute the mushrooms until they are golden all over. Keep cooking until you can see that the mushrooms have thrown out all their moisture – you need this to evaporate otherwise the juices will make your pie filling watery.
Melt the rest of the butter in a medium saucepan and add the flour. Stir around over a medium heat then take off the heat and start to stir in the milk mixture, adding a little at a time and stirring constantly to create a smooth sauce.
Put the pan back on the heat and bring to the boil, stirring all the time. Turn down to a simmer and add the tarragon, mustard, lemon juice, salt and pepper. Add the chicken and the cooked leeks and mushrooms and carefully stir together. Check for seasoning – you may even want to add a little more mustard. Heat everything through then leave it to cool a little.
Spoon the filling into the pie dishes and leave to cool. Damp the edge of the dishes with water and press the strip of pastry you prepared before around the rim. Dampen the strip and carefully put the lids on, pressing them firmly over the edge of the dish to get a good seal. Wet the leaves with water and place them on the pie tops, then quickly paint the pies with beaten egg.
Bake in the oven for 40 minutes until piping hot, puffed up and golden. Serve immediately.
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