Preheat the oven to 200C/400F/Gas 6.
Roll the puff pastry out on a floured surface into an 15cmx25cm/6inx10in rectangle and spread all over with the cream cheese.
Using a sharp knife, cut the pastry into 10 long, thin strips.
Wrap one pastry strip in a spiral around each asparagus spear and place onto a baking tray. Lightly brush each with beaten egg then scatter over the parmesan.
Bake the cigars in the oven for 15-20 minutes, or until the pastry has risen and is golden-brown.