Cook the eggs in a pan of boiling water for exactly 8 minutes. Meanwhile, sit a steamer or a colander over the eggs, put in the asparagus, cover and cook for 3-4 minutes until just tender. Drain the eggs and cool under cold water with the asparagus to prevent further cooking.
Melt the butter in a small pan then, with a wire whisk, beat in some lemon juice and season to taste.
Heat a ridged griddle pan. Cook the slices of Parma ham, two at a time in the hot pan for 30 seconds on each side. Drain on kitchen paper, then add the asparagus to the pan (making good use of the fat left from the Parma ham) for a minute or two to give light bar marks.
Shell and halve the eggs.
Arrange eggs on plates with the asparagus, topped with the crispy Parma ham. Drizzle over the lemon-butter dressing. Scatter the croutons on top and finish each one with a grinding of black pepper.