Whisk together yolks, lemon juice, salt and pepper together in a medium bowl until smooth and light. Whisk oil in by drops until the mixture starts to thicken and stiffen. As the sauce begins to thicken, when about one-third of the oil has been added, whisk in the oil more steadily, making sure each addition is thoroughly blended before adding the next. Should the oil stop being absorbed, whisk vigorously before adding more. Stir in mustard and salt and pepper to taste.
Serve immediately or refrigerate in a covered jar for 1 to 2 days.