Peel the asparagus, snap off the woody stem ends and finely chop the parsley.
Bring 3 saucepans of water to the boil.
Boil the baby new potatoes for around 15 minutes until tender. Simmer the asparagus for 10 to 15 minutes until it can be pierced with a fork. Boil the eggs (3 to 4 minutes for soft-boiled, 6 minutes for semi-soft and 8 to 10 minutes for hardboiled).
Plunge the eggs into cold water to quench and then peel.
Clarify the butter by putting it in a heavy saucepan over a low heat to melt. When the butter has completely melted use a spoon to skim off the white foam that has risen to the top. Take the butter off the heat and leave it to stand for 10 minutes. The milk solids will have settled to the bottom. Carefully pour off the clarified butter leaving the milk solids behind or strain through several layers of cheesecloth.
Serve the asparagus with the ham, baby new potatoes, clarified butter and boiled egg.