Bring a sauce pan of water to a boil with 1 tablespoon of white vinegar and gently place the three whole eggs in without cracking the shells. Boil 5 minutes, turn off burner and let sit 15 minutes in hot water. After 15 minutes, drain water and shake pan to crack shells. Peel under cold water, chop and set aside.
Place cauliflower and cubed yams in large sauce pan and cover with water. Add salt and bring to a boil. Simmer about ten minutes or until tender. Drain and leave in strainer draining.
In a small sauce pan, bring apple juice to a boil and boil until reduced to one tablespoon. Watch closely. The mixture will be thick and sweet. Pour into a small bowl and add cider vinegar, white vinegar, celery salt, pepper, poppy seeds and Dijon mustard. Stir in mayonnaise and onions.
Place drained, but still warm, cauliflower and yams in a large bowl.
Add mayonnaise mixture and stir.
Fold in chopped eggs and immediately refrigerate until chilled.