Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain and set aside to cool.

While the potatoes are cooking, whisk together sugar, 2 beaten eggs, and cornstarch in a saucepan; season with salt.

Stir in milk, vinegar, and mustard. Cook and stir over medium heat until thickened, about 10 minutes. Remove from heat and stir in butter. Refrigerate until cool, then stir in mayonnaise.

Peel and dice potatoes. Transfer to a large bowl; toss with hard-cooked eggs, onion, celery, and 1 teaspoon salt.

Stir dressing gently into the bowl of potato salad until evenly coated.