Place the asparagus in a steamer basket over 1 inch boiling water. cover tightly and steam until just al dente and bright green, about 2 mins.

Transfer to a colander and cool.

Preheat the oven to 450 with the rack in the center. Line a baking sheet with parchment paper and set aside.

Place 1 sheet of phyllo on a dry surface. Keep the remaining sheets covered with a clean, slightly damp towel. Brush lightly with melted butter and cut into 4 rectangular pieces, each 5 x 7 inches.

Place 1 pc. of prosciutto on the phyllo, lining it up along the short edge of the rectangle. Arrange an asparagus spear on top of the prosciutto, along the same short edge of the rectangle, letting the tip lay exposed beyond the top edge of the dough by 3/4 inch or so.

Sprinkle with 1/2 tsp parmesan. Roll up and secure the edge of the dough with additional butter, if necessary. Repeat with the remaining ingredients, transferring the straws onto the prepared baking sheet.

The straws may be made 1 to 2 hours ahead of time (up to this point) covered with plastic wrap and refrigerated. Before baking, sprinkle the top of the straws with the remaining cheese. Cover the asparagus tips with foil to protect them from the heat. Bake until golden brown - 5 to 8 minutes.

Serve warm, either whole or sliced into bite size pieces.