Prepare the asparagus for grilling. Brush the stalks with oil and lightly salt them.
Separate the whites and yolks of the cooked eggs and finely chop them. Put all the ingredients in a bowl and gently combine them with a rubber scraper. The yolks and oil will gradually emulsify. Season to taste with salt and plenty of pepper and add more vinegar if desired.
Grill the asparagus, lay it on a platter, and ladle the sauce over it.