Lay 1 sheet of the phyllo on a work surface with the short end directly in front of you. Brush it with butter and sprinkle with 1 tablespoon of the Parmesan cheese and a pinch of nutmeg. Set a wrapped asparagus on the short end of the phyllo and roll it up snugly. Brush the roll with butter, dust it lightly with more Parmesan and set it on a baking sheet. Repeat with the remaining ingredients, arranging the rolls at least 2 inches apart on the sheet.