In a saucepan of boiling salted water, blanch the asparagus until crisp-tender, about 2 minutes. Refresh under cold water and pat very dry with paper towels.
Season the asparagus spears with pepper. Roll them in the prosciutto; you will need about 1 1/2 slices to cover each spear.
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.
Preheat the oven to 400°. Bake the rolls on the top shelf of the oven for 10 to 12 minutes, or until golden brown and crisp. Let the rolls cool slightly before slicing them at an angle into bite-size pieces.