In a blender or food processor fitted with a metal or plastic blade, place egg, mustard, and vinegar.
Whirl until well blended (about 4 seconds).
With motor running on slowest speed, add oil just a few drops at a time at first, then increasing to a slow, steady stream about 1/16 inch wide.
If made ahead, cover and refrigerate.
Store for as long as 2 weeks.