FOR THE AIOLI:
1 head garlic, cloves separated, peeled and slightly crushed
2 egg yolks (at room temperature)
pinch coarse sea salt
2 cups extra virgin olive oil (at room temperature)
1-2 teaspoons water
In a marble mortar with a heavy pestle, pound the garlic and salt together into a paste. Add egg yolks and stir until they are light in color.
Slowly, drop by drop, begin to incorporate the olive oil, turning the pestle constantly. As the mixture begins to thicken, add the oil a little faster, always turning the pestle.
When it is quite thick (this could take up to 45 minutes!), add the water to loosen it. Continue mixing until the oil is completely mixed in. Cover and refrigerate until ready to serve.
WHILE THE AIOLI IS CHILLING, MAKE THE ASPARAGUS: Trim 2 lbs of asparagus spears; if the stalks are thick, peel them with a vegetable peeler. In a large saucepan, bring 1/2 inch of water to a boil. Add a good sprinkling of salt, and the asparagus. Cover, and cook for 2 minutes. Immediately remove the asparagus and plunge them into a bowl of ice water to stop the cooking. Then, drain and dry the asparagus, and set out on a platter with the aioli sauce in a bowl for dipping.