Cook the asparagus to your taste (I recommend that it retain some crispness.) Dry it well and put in the fridge to chill while you do the mayo.
Chop the shallots and put them with the vinegar in your smallest sauce pan. Boil furiously until the vinegar is reduced to about a tablespoon, then scrape it into the bowl of your food processor and let it cool for twenty minutes. Now break the egg into the food processor and add the salt and white pepper. Or you can season the mayo later, if you're apprehensive about amounts. Turn the processor on full blast, open the pour spout, and pour the oil in SLOWLY. When the oil is all poured in, you will have mayonnaise in the food processor. Let it chill for about half an hour, then slather it on the chilled asparagus on small serving plates. This makes a great appetizer, served with a good quality sparkling wine.