This sauce is made like a mayonnaise. Place the egg yolk in a mixing bowl and add salt and pepper to taste, the mustard and vinegar. Immediately begin whipping the mixture with a wire whisk or rotary beater. Add the oil, a few drops at a time, then continue to add it in a steady stream, beating constantly. The sauce should become thicker all the time.
Stir in the remaining ingredients, adding only enough water to make a thin sauce.