Preheat the oven to 230C/445F/Gas 8.
Heat a frying pan until hot and add the olive oil, onion and thyme and fry, for 2-3 minutes, until the onions are golden and softened.
Place the beef mince into a bowl with the mustard powder and beef stock. Add the fried onion mixture and season well with salt and freshly ground black pepper. Mix well to combine.
Roll out the puff pastry on a clean, floured surface to 5mm/¼in thick and cut out four 15cm/6in diameter circles.
Place a spoonful of the mince mixture into the centre of each pastry circle. Brush the outer edge of each pastry circle with the beaten eggs. Fold over the pastry in half, to create a pasty shape and crimp the edges together well to seal.
Brush the pastry with the beaten eggs and season with salt and freshly ground black pepper.
Place onto a lightly greased baking tray and place into the oven to bake for 15 minutes.
Reduce the heat of the oven to 180C/385F/Gas 4 and cook for 45 minutes, or until golden brown and completely cooked through.
These pies can be served hot, warm or cold.
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James Martin takes a look back at some his favourite recipes from Saturday Kitchen.