Place chopped potatoes in a large pot and cover with cold water. Add a pinch of salt and bring to a boil. Reduce heat and simmer for about 10–12 minutes, or until potatoes are fork-tender but not mushy. Drain and let cool slightly.
While the potatoes are cooking, place the eggs in a saucepan and cover with cold water. Bring to a boil, then turn off the heat and let sit, covered, for 10–12 minutes. Drain and transfer to a bowl of cold water. Peel and chop the eggs once cool.
In a large bowl, whisk together mayonnaise, mustard, vinegar, salt, and pepper until smooth.
Add the cooked potatoes, chopped eggs, celery, and onion to the bowl with the dressing. Gently fold everything together until well combined. Taste and adjust seasoning if needed.
Cover and refrigerate for at least 1 hour before serving. Sprinkle with paprika and parsley just before serving, if desired.
Notes
Yukon Gold potatoes hold their shape best, but red potatoes work well, too.
Let the potatoes cool slightly before mixing so the dressing stays creamy.
Potato salad tastes even better after chilling—make it a few hours ahead if you can.
Store leftovers in the fridge for up to 4 days.
Garnish with paprika and parsley for a classic finishing touch.