First, make the salsa: Put the parsley, garlic, walnuts, lemon zest and juice into the bowl of a food processor. Whizz until coarsely chopped.
Add half the Parmesan to the bowl. Blend again. With the motor still running, trickle in the oils. Stop blending while it’s still a coarse-looking purée. Adjust the seasoning. Cover and chill.
Place the asparagus in boiling water and season with a little salt. Simmer for 3-5 minutes until al dente, and drain well.
To assemble: place the prosciutto on each plate. Place the asparagus on top with the tips sticking out. Drizzle or brush the spears generously with olive oil, season, and fold over the prosciutto to cover the asparagus.
Spoon a dollop of salsa on top and scatter parmesan shavings over each portion.