Preheat the oven to 425°F. Place an oven-safe rack on a foil-lined, rimmed baking sheet. Cut each prosciutto slice into quarters lengthwise. Place the asparagus spears in a shallow bowl.
In a small bowl, combine the oil, garlic, lemon zest, red pepper flakes, and black pepper. Pour the oil mixture over the asparagus, rubbing it on thoroughly. Wrap each spear with prosciutto and place on the prepared rack. Spoon any of the remaining oil mixture from the bowl over the asparagus.
Roast until the asparagus is tender and the prosciutto is crispy, 30 to 35 minutes. Serve hot with parsley, lemon wedges, and extra pepper flakes.