Preheat the oven to 425°F, and coat a shallow baking sheet with nonstick spray.
Trim 1 to 1-1/2 inches from the bottom of the asparagus spears, wash and pat dry.
Slice the prosciutto lengthwise into thirds. Working at an angle, wrap the middle section of each asparagus spear with a strip of prosciutto (like the stripes on a barbershop pole) and arrange them in a single layer on the prepared baking sheet.
In a small bowl, whisk the olive oil and balsamic vinegar together. Brush about half of the mixture onto the asparagus and grind some black pepper over the top. Roast for 5 minutes, or until the asparagus starts to wilt and develop a little brown color.
Remove from the oven, brush again with the remaining oil and vinegar mixture, then return to the oven for another 3 to 5 minutes, or until the thickest part of the asparagus is tender. Grind a little more pepper over the top if desired.
Transfer to a plate and serve immediately.
Notes
For best results, try to choose asparagus spears that are about 3/8-inch in diameter at the thick end and keep a close eye on them in the oven to avoid overcooking.