Preheat the oven to 375º. Thaw the puff pastry dough for an hour on the counter or until softened. Dust a surface with flour and roll out the puff pastry dough. Using a pizza cutter, cut thin strips of pastry dough.
Assemble the roll ups by taking 1-2 asparagus stalks and wrapping the puff pastry around and up in a spiral. Repeat until all the dough is used. Lay the puff pastry rolls flat on a baking sheet, seam side down.
Melt butter and mix with the dried basil, then take a pastry brush to brush the melted butter mixture on top of each of the pastry rolls. Bake for 25-30 minutes or until golden brown.
Notes
Remember to let the puff pastry thaw for at least an hour on the counter before attempting to use it. It will crack and be difficult to spread and roll out if it is not properly thawed.Dust the counters before rolling out the pastry dough, as it will help with any stickiness.Tuck the tail of the pastry strand underneath the asparagus to prevent it from unwrapping.Snap or cut off 1-2 inches of the ends of the asparagus to discard any woody ends before using.