Wash asparagus and break off tough ends.
Fill a large bowl with water and ice.
Bring another pot of water to a rolling boil.
Add asparagus and boil for 2-3 minutes (thick stalks will take 3 minutes)
Remove asparagus and submerge in ice water for about 1-2 minutes.
Pat asparagus dry.
Preheat oven to 375 degrees.
Cut phyllo pastry dough into strips. Unroll 1 packet of dough and cut the dough in half. Then, cut each half down the middle. Reserve remaining dough for another use.
Keep unused dough strips covered with plastic wrap and a damp towel. If not using phyllo dough for an extended period of, keep it in the refrigerator.
Using a pastry brush, spread melted butter over a phyllo dough strip.
Place asparagus at one end and roll up jelly style.
Place asparagus on a cooking sheet coated with cooking spray.
Repeat for each asparagus stalk.
Lightly brush butter over the rolled asparagus stalks on the cooking sheet.
Bake for about 15 minutes or until pastry dough is lightly browned.