Put the egg, garlic, lemon juice, parsley, green onions, and relish in a food processor or blender and process for 15 seconds. With the motor running, pour the oil through the feed tube in a slow steady stream. Add the cayenne, mustard, and salt and pulse once or twice to blend. Cover and let sit for 1 hour in the refrigerator before using. Best if used within 24 hours.
Recipe from Everyday Is A Party Cookbook, by Emeril Lagasse, with Marcelle Bienvenu and Felicia Willett, published by William Morrow, 1999