Preheat oven to 400 degrees. Line a baking sheet with parchment paper or a silicone mat for easy cleanup.
Remove the woody, tough ends from the asparagus. To do this, grab a handful of stems (5-6 at a time) and start to fold near the bottom of the stem. Each stem should break at the spot where it starts to toughen.
Cut each piece of prosciutto into quarters (you should have about 16 pieces). Working with one asparagus stem at a time, wrap a piece of prosciutto around the middle of the stem. Place on prepared baking sheet and repeat with remaining prosciutto and asparagus.
Brush the wrapped stems lightly with olive oil, concentrating most on the flowery tops which dry out easily. Sprinkle with pepper to taste (I like 1/2 teaspoon).
Bake until the asparagus stems are tender and the prosciutto is crisp, about 20 minutes. Serve warm or at room temperature.
Slightly thicker asparagus works best: Look for asparagus spears that are about the diameter of your little finger, instead of the pencil-thin variety that you can find year-round.
Prosciutto substitutions: Try bacon or Spanish Serrano ham. You could also try pancetta, another Italian pork product, if it is sliced thin enough (pancetta is also salt-cured, but not smoked, so it needs to be cooked before eating).
Bundles: Wrap 5-6 spears together with one whole slice of prosciutto, and roast as directed. This makes a fabulous individual vegetable side for guests.
Balsamic drizzle: Drizzle a small amount of syrupy balsamic reduction (a thicker concentrate of balsamic vinegar) over the platter of cooked asparagus just before serving.
Make ahead: You can prepare these the day before you need them and store them in the refrigerator.
Leftovers: Store in an airtight container in the refrigerator. You can eat the prosciutto wrapped asparagus cold, at room temperature, or reheated in the oven.