Peel the asparagus and cut off the woody ends. Wash the asparagus and cook in boiling salted water for about 20 minutes. Wash potatoes and cook in water for about 20 minutes. Quench cold and peel.
Drain the asparagus and divide into 8 portions. Wrap 2 slices of ham around each portion. Heat 2 tablespoons of oil in a frying pan and fry the asparagus parcels one after the other. Wash the parsley, dab dry, pluck the leaves from the stalk and chop finely.
Sprinkle over the potatoes. Arrange asparagus parcels and potatoes on a plate. Heat the remaining olive oil and drizzle over the asparagus. Serve garnished with basil if desired.