Drop tiny new potatoes in boiling, salted water and cook, timing carefully after the water returns to a boil for six minutes. Potatoes should be no larger than an English Walnut. Otherwise, cut them into pieces about that size. After cooking, drain potatoes well, rinse under cold water, and bring to room temperature.

In saucepan, beat eggs. Stir in sugar and vinegar. Melt butter in small pan and reserve.

Place the egg mixture over low heat and cook stirring constantly until thickened to the consistency of heavy cream. Remove from heat.

Stir in the melted butter, along with celery seed and dry mustard. Place pan in a larger pan of cold water to cool the dressing quickly and prevent overcooking. When dressing is cooled to room temperature, combine with mayonnaise to make enough to coat the potatoes. Add additional mayonnaise as needed.