Step 1: Cook the Potatoes: Place the cubed potatoes in a large pot and cover with cold water. Bring to a boil and cook until tender, about 12-15 minutes. Drain well and let cool slightly.
Step 2: Hard-Boil the Eggs: Place the eggs in a saucepan and cover with cold water. Bring to a boil, then remove from heat, cover, and let stand for 12 minutes. Drain and rinse with cold water. Peel the eggs and chop them into small pieces, reserving one yolk for garnish.
Step 3: Prepare the Dressing: In a large bowl, whisk together the mayonnaise, Dijon mustard, white vinegar, sweet pickle relish, red onion, celery, paprika, and celery seed. Season with salt and pepper to taste.
Step 4: Combine Ingredients: Gently fold the cooled potatoes and chopped eggs into the dressing until well coated.
Step 5: Chill and Serve: Cover the salad and refrigerate for at least 30 minutes to allow the flavors to meld. Before serving, garnish with reserved egg yolk crumbled on top and chopped fresh parsley, if desired.
Optional Tips: For a tangier flavor, add an extra tablespoon of white vinegar or a squeeze of lemon juice. For a smoky flavor, use smoked paprika. If sweet pickle relish is not available, finely chop dill pickles and add a pinch of sugar to the dressing. To reduce the fat content, use light mayonnaise or a combination of mayonnaise and Greek yogurt.