To clarify the butter, heat the butter in a small, heavy-bottomed saucepan over medium heat until it melts and froths up. Simmer it for about 5 minutes, or until the froth subsides and the butter looks clear. Don't let it burn. Strain the butter through a fine-mesh strainer, a triple layer of cheesecloth, or a coffee filter. Let the butter cool for 5 minutes, if the butter is too hot it will curdle the egg yolks. Combine 3 egg yolks and 3 tablespoons butter in a bowl, and whisk off heat for 1 minute, until frothy. Place yolks on stovetop over medium-low heat and beat until thick. Meanwhile drain cooked asparagus, and toss with 1 tablespoon of butter. Remove yolks from heat, if they have not been removed already and whisk in remaining butter. Stir in the lemon juice, salt and pepper. Plate the asparagus and sauce.
Bring about 6 quarts of water to a rapid boil in a covered pot large enough to hold the asparagus. Cut the bottom section- usually about 1 to 2 inches off the asparagus stalks with a sharp knife. Peel the asparagus by laying them flat, one at a time, on a cutting board. If the asparagus are thinner than 1/2-inch, use a vegetable peeler and peel the asparagus starting at the base of the tip and peeling them all the way down to the base, eliminating the fibrous peel and revealing the pale green flesh. If the asparagus are very thick or woody, use a paring knife and start peeling from the base. When ready to cook, toss the salt into the boiling water and carefully lower in the asparagus. Turn the heat to low and simmer the asparagus, uncovered, until the spears are easily penetrated with a knife, usually after about 5 minutes but from 1 minute for very thin asparagus to 12 minutes for the very thickest. If serving cold asparagus, plunge the hot cooked asparagus into ice water or rinse under cold water in a colander. Pat dry.