Place 1 puff pastry sheet on a work surface. Cut puff pastry crosswise into thirds to form 3 (4 1/2 x 9inch) rectangles.
Take 1 asparagus spear and wrap one prosciutto strip around it. Place wrapped asparagus across 1 short end of each puff pastry rectangle; roll up jelly-roll fashion.
Arrange rolls on a baking sheet; brush rolls with melted butter and garlic salt and freshly grated parmesan to the top of these before baking.
Bake at 450° for 10 minutes or until pastry has puffed up and is golden brown.
Serve warm or at room temperature.