Put potatoes and the three eggs in pot and cover with cold water. Bring to a boil, turn the heat down, cover loosely, and simmer until potatoes are easily pierced with a fork (15 minutes or so)
Drain the potatoes. Fish out the eggs, peel, and chop them.
When they are cool enough to handle, cut them into bite-sized pieces and mix them up with the olive oil.
Add the chopped eggs, celery, onion, and parsley.
Mix together the dressing ingredients and add to potatoes. Salt and pepper to taste. Refrigerate and serve cold.