In a small bowl beat the egg yolks until thick with the mustard, salt, and pepper. Add the oil, drop by drop, whisking constantly. After adding 2 tablespoons of the oil, the mixture should be quite thick. Add the remaining oil more quickly, a tablespoon at a time, or pour from a jug in a very slow stream, whisking constantly. Stir in the vinegar. In a clean bowl whip the egg whites until stiff. Fold the egg whites into the mayonnaise. You can substitute 1/4 cup unsweetened whipped cream for the beaten egg whites.
