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Make the dressing – Whisk together the 2 well-beaten eggs, sugar, cornstarch and ½ teaspoon kosher salt in a medium saucepan.
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Whisk in the cider vinegar, evaporated milk, and Dijon mustard. Heat the pot to medium, stirring frequently, until the sauce is thickened – this should take about 10 minutes. Do not let the mixture boil.
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Remove the pan from the heat and whisk in the butter, piece by piece. Refrigerate the sauce until it has stiffened, then whisk it together with the mayonnaise. Cover the dressing and keep refrigerated.
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Put the potatoes in a large saucepan or soup pot and cover with cold water. Bring the pot to a boil and cook the potatoes until they are fork-tender, about 20 minutes. Drain them and let them cool.
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Peel the cooled potatoes and dice them into 1-inch cubes. In a large bowl, toss the cooked potatoes with the chopped onion, celery, chopped hard boiled eggs, 1 teaspoon kosher salt and the white pepper.
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Fold the chilled dressing into the potato mixture and stir until everything is well coated with the dressing. Cover the bowl and chill at least 1 hour, and preferably overnight.