Step 1: Cook the Potatoes: Place the cubed potatoes in a large pot and cover with cold water. Add a pinch of salt. Bring to a boil and cook until the potatoes are tender but not mushy, about 12-15 minutes. Drain the potatoes and let them cool slightly.
Step 2: Hard-Boil the Eggs: While the potatoes are cooking, place the eggs in a separate saucepan and cover with cold water. Bring to a boil, then remove from heat, cover, and let sit for 10 minutes. Transfer the eggs to an ice bath to stop the cooking process. Peel the eggs and chop them coarsely.
Step 3: Prepare the Dressing: In a large bowl, whisk together the mayonnaise, Dijon mustard, and apple cider vinegar until smooth.
Step 4: Combine Ingredients: Gently fold the slightly cooled potatoes, chopped eggs, celery, red onion, and parsley into the dressing. Be careful not to mash the potatoes.
Step 5: Season and Chill: Season the salad with salt and freshly ground black pepper to taste. Cover and refrigerate for at least 2 hours, or preferably overnight, to allow the flavors to meld.
Step 6: Serve: Before serving, give the salad a gentle stir. Garnish with additional fresh parsley, if desired. Serve cold.
Optional: For a tangier flavor, add a tablespoon of sweet pickle relish to the dressing. Chopped bacon can also be added for a smoky flavor. For a lighter dressing, use half mayonnaise and half plain Greek yogurt.