For the rough puff pastry, place the flour in a mound on a clean work surface and make a well in the centre. Place the butter and salt in the well and work them together with the fingertips of one hand, gradually drawing the flour into the centre with the other hand.
When the cubes of butter have become small pieces and the dough is grainy, gradually add the iced water and mix until it is all incorporated, but don’t overwork the dough – you should have a marbled effect with the butter without mixing it in completely.
Roll the mixture into a 2.5cm/1in-thick rectangle, wrap in cling film and refrigerate for 20 minutes.
When the pastry is chilled, flour the work surface and roll out the pastry into a 40x20cm/16x8in rectangle.
Fold the top third down to the centre, then the bottom third up and over that. Give it a quarter-turn.
Roll the block of pastry into a 40x20cm/16x8in rectangle as before, and fold it into three again. These are the first two turns. Rest the pastry in the fridge for at least 20 minutes between turns. Repeat two more times to make four turns.
Wrap the pastry in cling film and refrigerate for at least 30 minutes before using.
For the pie, preheat the oven to 200C/180C Fan/Gas 6.
Heat a large ovenproof frying pan until hot, add the butter and when the butter is foaming, add, the shallot and garlic and fry for a minute. Add the chicken and fry until just coloured.
Add the mushrooms and fry over a high heat for 2-3 minutes, or until just softened. Add the Madeira and flambé by tipping the pan towards the flame or carefully lighting using cooks' matches. (CAUTION: make sure there are no flammable materials above the pan when flaming.)
Add the chicken stock and bring to a simmer, then add the tarragon and cream and simmer for five minutes. Add salt and pepper to taste and then set aside to cool.
Roll out the pastry until it is 5cm/2in wider than the ovenproof frying pan and about 4-5mm thick. Brush the edges of the frying pan with beaten egg and then lay the pastry over the top of the pie filling and crimp at the edges. Trim away any excess pastry and brush the top of the pie with the remaining egg. Use any pastry trimmings to make leaves to decorate the top of the pie.
Bake for 25 minutes, or until the pastry is crisp and golden-brown and the filling bubbling.