In blender or food processor, place shallot, vinegar, mustard, juice, salt and pepper. Blend or process on medium for 30 seconds or until mixture is combined. With blender or food processor running, slowly add oil in a very, very thin stream.* Blend until mixture is well combined. Adjust seasoning if desired. Place in air tight container and refrigerate for at least 1 hour. Store in Sub-Zero refrigerator.
*Some food processors have a small opening in small food pusher. Pour oil into it so oil will slowly enter the food processor bowl.