Preheat the oven to 200°C, fan 180°C, gas 6. Roll out the pastry onto a floured surface, and cut out 4 x 18cm circles – use a side plate as a template. Put on baking trays and chill in the fridge while you prepare the filling.
Heat the oil in a pan, add the onion, carrot and potato. Cook over a medium heat for 10 minutes, until beginning to soften. Stir in the tomato purée with the dissolved gravy granules. Remove from the heat and stir in the leftover roast beef. Season with freshly ground black pepper.
Divide the filling into four and spoon onto one side of each pastry circle, leaving a 1cm edge. Brush the edges with a little beaten egg and fold the pastry over the filling to make half-moon shapes. Twist the edges or pinch together to seal the pasties.
Brush the tops of the pasties with the rest of the egg glaze. Bake for 30 minutes, until golden.
Serve the warm pasties with the steamed broccoli.