Heat the oven to 200C (180C fan) 400F, gas 6.
Peel the lower third of the asparagus spears and place in boiling, salted water. Simmer gently for about 10 minutes, then drain, refresh in cold water and drain thoroughly.
Wrap 2 asparagus spears in a slice of prosciutto and lay side by side in an ovenproof baking dish. Sprinkle with a little freshly ground pepper.
Mix the parmesan with 3 tbsp olive oil and scatter over the asparagus. Bake in the oven for 6-8 minutes.
Wash and sort the arugula, removing any hard stalks, and arrange on plates. Drizzle with 2 tbsp olive oil and vinegar. Sprinkle with salt and pepper and lay the asparagus on top. Serve immediately.