Crack each egg into a cup. Fill a deep saucepan with water and bring to the boil. Reduce to a simmer and add the vinegar and 1 teaspoon of salt. Stir with a spoon to make a whirlpool and drop an egg into the centre. Cook until the white is firm and the yolk runny, 3–4 minutes.
Remove with a slotted spoon and transfer to a bowl of cold water. Repeat with the remaining eggs. These can be done in advance, and reheated for serving.
Bring a large saucepan of water to the boil and add 1 teaspoon of salt. Snap off the base of the asparagus spears where they become naturally tender, or trim and peel the ends. Tie into batches of spears of equal thickness and poach until tender, 2–4 minutes, according to their size. It is better if they are tender rather than crunchy. Discard the string.
To make the dressing, place the cheese in a bowl and add half the lemon juice. Mash with a spoon to form a paste. Gradually incorporate more lemon juice to give a smooth paste, without it becoming too sharp. Now gradually add the oil in small amounts to give a creamy mayonnaise-like mixture. Season to taste with the black pepper. Alternatively, place dressing ingredients in a food processor and whiz to form a smooth paste. The consistency should be runny but not entirely liquid.
To serve, gently lower the eggs into the asparagus cooking water to reheat. Toss the asparagus with half of the dressing, coating well. Place on a serving plate. Using a slotted spoon, remove the eggs from the water and place on top of the asparagus. Drizzle the remaining dressing over the eggs and around the plate, and then sprinkle the celery leaves