Place 24 trimmed asparagus spears and ¼ cup boiling water in large roasting pan covered with foil.
In a preheated 400°F oven, steam asparagus until tender, 10 to 15 minutes; transfer to paper towels to drain, and wipe pan dry.
Assemble 12 thin slices prosciutto (8 ounces), each cut in half lengthwise, and ½ cup freshly grated Parmesan cheese.
On waxed paper, place 1 thin strip prosciutto and sprinkle with 1 teaspoon freshly grated Parmesan; roll prosciutto around spear—it will overlap slightly to cover the spear.
Repeat with remaining asparagus, prosciutto, and Parmesan.
Roast until asparagus is heated through and prosciutto just begins to brown, about 10 minutes.