Roll out the pastry thickly on a lightly floured surface and trim to a 23 × 30 cm (9 × 12 inch) rectangle. Transfer to an oiled baking sheet and use a little beaten egg to glaze. Mark a line 2.5 cm (1 inch) in from the edge, then prick the inside rectangle with a fork.
Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 10 minutes. Press down the centre with the back of a fork, then bake for 5–10 minutes more until the pastry is cooked through. Press down the centre once more.
Meanwhile, trim 2.5 cm (1 inch) from the base of the asparagus, then trim the spring onions to the same length. Toss the asparagus and spring onions in the oil and plenty of salt and pepper, then cook on a preheated ridged frying pan for 5 minutes, turning, until just cooked.
Beat the mascarpone with the garlic, Parmesan, remaining beaten egg and salt and pepper. Spoon into the centre of the pie case and spread into an even layer. Arrange the asparagus and spring onions alternately on top and sprinkle with a little extra Parmesan.
Bake for 10–15 minutes until the filling is just set, Check after 10 minutes and cover with kitchen foil if the pastry seems to be browning too quickly.