Boil potatoes until tender, about 15 minutes. Drain; let cool. Cube potatoes into large pieces and combine with chopped onion. Roughly chop eggs into small pieces. In a small bowl, combine eggs, mayonnaise, lemon juice, lemon rind, and garlic. Stir the mayonnaise mixture into the potatoes and onions, until coated. Fold in chopped parsley. Serve chilled.