Lightly brush 1 sheet of filo pastry with butter and sprinkle with Parmesan cheese. Roll 2 asparagus spears up with the prepared filo dough, and place seam-side down on a baking tray. Repeat until all the asparagus spears are rolled. Brush each roll with butter and sprinkle with Parmesan cheese.
Cook in the preheated oven until the filo is golden brown and crispy, 15 to 18 minutes.