How to Make It
Preheat the oven to 350°. Cut the asparagus spears into 6-inch lengths; reserve the rest of the asparagus for another use. In a medium saucepan of boiling salted water, cook the asparagus for 1 minute; drain well. Transfer the asparagus to a rimmed baking sheet; pat thoroughly dry and let cool completely. Wrap each asparagus in prosciutto.
On a work surface, cut the phyllo into 8-by-6-inch rectangles. For each straw, lightly brush a phyllo rectangle with butter; set a prosciutto-wrapped asparagus at one end and roll it up in the phyllo. Set the straw on the baking sheet, seam side down. Repeat to form the remaining straws, arranging them at least 1 inch apart on the baking sheet. Brush the straws with the remaining butter and sprinkle with the Parmigiano-Reggiano. Bake the straws for 25 minutes, or until golden. Let cool slightly before serving.