Snap off the tough ends of the asparagus. Unwrap the phyllo and cut the stack in half lengthwise. Reserve 1 stack for later use. Cover the phyllo with a damp towel to keep it from drying out. Take 1 sheet of phyllo and brush lightly with some melted butter. Sprinkle with some Parmesan. Place 2 to 3 asparagus spears on the short end of the sheet. Roll up, jelly-roll style. Place each piece, seam side down, on a baking sheet. Brush with more melted butter and sprinkle with more Parmesan. Repeat until all the asparagus spears are used up. Place baking sheet in oven and bake for 15 to 18 minutes, or until golden brown and crispy.