For the filling
Preheat the oven to 200°C/400°F/Gas mark 6.
To make the pastry, sift the flour and salt together into a large bowl. Add the butter, and rub it in with your fingertips until the mixture resembles coarse breadcrumbs. Add just enough of the cold water to form a dough. Knead briefly until smooth. Wrap in cling film and leave to chill in the refrigerator for 30 minutes.
To make the filling, melt half the butter in a large frying pan over a low heat. Add the leek, onion and carrot, and cook gently for 7–8 minutes until the vegetables are softened. Remove from the heat and leave to cool slightly.
Put the vegetable mixture into a bowl, and add the potato, cod, vinegar, remaining butter, cheese and tarragon. Season with salt and pepper.
Remove the pastry from the refrigerator, and roll out thinly. Using a pastry cutter, press out four 19cm/7 1⁄2in discs. Divide the filling between the discs.
Moisten the edges of the pastry, and fold over to form a half-moon. Pinch and crimp the edges to seal. Put the pasties on a lightly greased baking tray. Brush generously with the beaten egg.
Bake in the oven for 15 minutes. Remove from the oven, and brush again with the egg glaze. Return to the oven for a further 20 minutes until the pastry is golden. Serve warm.