Cut phyllo dough in half, lengthwise. Cover with moist paper towel while using.
Use two layers phyllo for each "bundle". Brush melted butter over dough and sprinkle with Parmesan.
Place about 3 stalks of aspargus cross-wise over dough so that tips are over the edge. You will need to trim the asparagus so it fits "sideways" over the dough. Roll up and brush melted butter and more parm over top. Place seam-side down on baking sheet.