Trim the woody ends from the asparagus. Spread the spears in a single layer in a shallow baking pan, drizzle with olive oil, sprinkle with salt, and roll to coat thoroughly.
Roast the asparagus until lightly browned and tender, about 10 minutes, giving the pan a good shake about halfway through. Spread the roasted asparagus on a serving platter. Grind a generous amount of pepper over and shave the Asiago into wide flakes on top. Tear the prosciutto into ragged pieces and scatter on top Serve warm or at room temperature.