Place the potatoes into a large pot, and fill with enough water to cover. Bring to a boil, and cook for about 20 minutes, or until easily pierced with a fork. Drain, and set aside to cool.
While the potatoes are cooking, whisk together 2 eggs, sugar, cornstarch, and salt in a saucepan. Stir in the vinegar, milk, and mustard. Cook over medium heat, stirring frequently, until thickened, about 10 minutes. Remove from heat, and stir in the butter. Refrigerate until cool, then stir in the mayonnaise.
Peel the potatoes if desired, and cut into medium dice. Place in a large bowl, and toss with the onion, celery, carrots, celery seed and hard-cooked eggs. Gently fold in the dressing. Refrigerate until serving. I personally like this to sit for at least a day before serving to let the flavors blend, but you may serve it as soon as it is chilled.
