Preheat the oven to 400° F. Prepare an ice-water bath in a large bowl. Bring a pot of salted water to a boil. Add the asparagus and cook until slightly tender but still very green, about 30 seconds. Gently lift the asparagus out and put in the ice-water bath to cool. Drain and pat dry.
Season each asparagus stalk with salt and pepper. Using about 1 1/2 slices prosciutto for each asparagus stalk, tightly wrap each stalk in the prosciutto.
Place a sheet of phyllo on a work surface. Brush with melted butter and sprinkle with Parmesan, nutmeg, salt and pepper. Place an asparagus wrapped in prosciutto along the shorter edge of the dough. Tightly wrap the asparagus in the phyllo and trim off any leftover dough. Repeat with the remaining asparagus. Brush each roll with butter and sprinkle with or roll them in Parmesan. Place the rolls on a greased baking sheet and bake for 5 to 7 minutes, until golden brown. Cut each roll at an angle into 8 pieces and serve immediately.