Place whole waxy potatoes in a medium pot and cover with cold water by 1 inch. Add 1 teaspoon salt and bring to a boil over high heat. Reduce heat to medium and cook 15-20 minutes until a fork pierces with slight resistance. Drain immediately in a colander and let cool 10 minutes.
2 lbs waxy potatoes, 1 tsp salt
In a large mixing bowl, whisk together mustard, white vinegar, ½ teaspoon salt, and black pepper until smooth. Add mayonnaise and whisk until fully combined with no streaks.
0.75 cup mayonnaise, 2 tbsp yellow mustard, 1 tbsp white vinegar, 0.5 tsp salt, 0.25 tsp black pepper
While the potatoes cool, dice celery and onion into ½-inch pieces. Chop hard-boiled eggs and mince fresh parsley or dill.
2 stalks celery, 0.25 cup red onion, 3 hard-boiled eggs, 2 tbsp fresh parsley
Cut cooled potatoes into ¾-inch chunks, leaving skin on if using red potatoes. Add potatoes, celery, onion, and eggs to the dressing bowl. Fold gently with a rubber spatula until all ingredients are coated but potatoes hold their shape.
2 lbs waxy potatoes, 2 stalks celery, 0.25 cup red onion, 3 hard-boiled eggs
Stir in fresh herbs and taste for salt and pepper, adjusting if needed. Cover the bowl with plastic wrap and refrigerate for at least 1 hour before serving to let flavors meld and the dressing thicken.
2 tbsp fresh parsley