Put potatoes in a large saucepan with water to cover. Bring to a boil and cook, covered, until tender, 15 to 20 minutes. Drain; rinse with cold water. Let potatoes cool.
Stir together yogurt, mayonnaise, mustard, salt, and pepper in a large bowl. Stir in cauliflower and fresh parsley. Add cooled potatoes; toss gently to coat. Chill, covered, at least 1 hour or up to 24 hours.
Healthier Creamy Potato Salad · Dinner Match Lab | Dinner Match Lab