Lightly grease six metal pie tins measuring 9cm (3½inches) along the base and 3cm (1¼inches) deep.
Heat 2tablespoons of the oil in a large frying pan and brown the steak in batches. Remove from the pan. Heat the remaining oil in the same pan, add the onion and garlic and stir over medium heat until golden brown. Add the flour and stir over medium heat for 2 minutes, or until well browned. Remove from the heat and gradually stir in the combined wine and stock.
Return to the heat and stir until the mixture boils and thickens. Return the meat to the pan, add the bay leaves and thyme and simmer for 1 hour. Add the carrot and simmer for another 45 minutes, or until the meat and carrot are tender and the sauce has thickened. Season, then remove the bay leaves and thyme. Allow to cool.
Preheat the oven to 200°C (400°F/Gas 6). Divide the shortcrust pastry into six portions and roll out each piece between two sheets of baking paper to a 25cm (10inch) square, 3mm (⅛inch) thick. Cut a circle from each shortcrust sheet big enough to line the base and side of each pie tin. Place in the tins and trim the edges. Line each pastry shell with baking paper and fill with baking beads or uncooked rice. Place on a baking tray and bake for 8 minutes. Remove the paper and beads and bake for another 8 minutes, or until the pastry is lightly browned. Allow to cool.
Divide the puff pastry into six portions and roll each piece between two sheets of baking paper to a square. Cut circles from the squares of dough, to fit the tops of the pie tins. Divide the filling evenly among the pastry cases and brush the edges with some of the beaten egg. Cover with a puff pastry round and trim any excess pastry, pressing the edges with a fork to seal. Cut a slit in the top of each pie. Brush the pie tops with the remaining beaten egg and bake for 20–25 minutes, or until the pastry is cooked and golden brown.