Trim the bottoms of the asparagus stalks and peel with a vegetable peeler. Bring a large pan of salted water to a boil and drop in the asparagus. Simmer for 3 minutes and have a large bowl of iced water ready.
Using a large slotted spoon, lift out the asparagus spears carefully. Place immediately into the iced water and leave for 5 minutes, then carefully drain.
Slice the avocado and mix gently with a third of the dressing. Season well. Slice the tomatoes thinly and season. Allow to stand for 10 minutes then drizzle with another third of the dressing and mix in the basil.
Arrange 2 slices of ham on each of four large plates. Divide the asparagus, tomato and avocado between the plates. Drizzle the last of the dressing over the asparagus and sprinkle over the chives. Season with coarsely ground pepper and serve.