Peel the stem before cooking, always holding onto the end of the stem which is harder than the rest of the asparagus.
Tie the asparagus together with kitchen twine in order to avoid breaking the delicate tips during cooking.
To check that the asparagus are cooked, touch them: they should be “al dente,” soft but not mushy. When they are ready, remove the pan from the heat but keep the asparagus in the boiling water.
Cook two eggs per person. Try not to break the yolk and do not cook the white so long that it becomes rubbery.
While the eggs are cooking, drain the asparagus, cut the twine, and arrange on plate. Cover the asparagus tips with grated Parmigiano Reggiano cheese. When the eggs are cooked, place them on the asparagus tips and serve drizzled with melted butter.