Heat the oil in a large frying pan and fry the chicken, stirring, until beginning to colour. Add the onion and fry until the chicken is golden and the onion softened. Stir in the garlic, then mix in the flour. Add the wine, stock, thyme and a generous sprinkle of salt and pepper. Bring to the boil, stirring, then cover and simmer for 30 minutes.
Heat the butter in a small frying pan, add the mushrooms and fry until golden. Add to the chicken and leave to cool.
Make the pastry. Add the flour, mustard and a little salt and pepper to a mixing bowl. Add the fats and rub in using your fingertips or using an electric mixer until you have fine crumbs. Gradually mix in enough of the water to form a soft but not sticky dough. Knead lightly, wrap in clingfilm and chill for 15 minutes.
Reserve one-third of the pastry, then cut the rest into 4 pieces. Roll each piece out thinly, then line 4 buttered individual springform tins, 10 cm (4 inches) in diameter and 4.5 cm (1¾ inches) deep. Roll out the reserved pastry thinly and cut out lids, using the tins as a guide.
Spoon the chicken filling into the pies, brush the top edges with beaten egg, then add the lids and press the pastry edges together. Flute the edges and bake on a baking sheet in a preheated oven, 190°C (375°C), Gas Mark 5, for 30 minutes until golden. Leave to stand for 5 minutes, then loosen the edges, transfer to a plate and remove the tins. Serve with green vegetables.