Snap off tough ends of asparagus. Unwrap phyllo and cut the stack into half lengthwise. Reserve 1 stack for later use. Cover the phyllo with a damp towel to keep if from drying out. Take 1 sheet of phyllo and brush lightly with some melted butter. Sprinkle with some parmesan. Place 2-3 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 15-18 minutes or until golden brown and crispy. When done let cool and drain on paper towels.
*Don't crowd on pan or they will steam and not crisp.
These can be prepared ahead and set in refrigerator overnight and then cooked. Cover well and remove cover before baking.