Place the potatoes in a big pot with enough water to cover by 1-inch.
Season liberally with salt and bring to a boil.
Cook until the potatoes are just tender when pierced, about 5 to 6 minutes. Once a knife can easily pierce one of the potato pieces, they are ready. Don't overcook!
Drain the potatoes.
Place the chopped celery and onion in the bottom of a large bowl. Add the hot potatoes and stir with a large wooden spoon until fully combined.
To facilitate cooling, spread the potatoes out onto a large baking sheet.
Meanwhile, in a medium bowl, mix together the mayonnaise, Dijon, 1 tsp salt, a pinch of black pepper, vinegar, lemon juice, and dill. Whisk until fully combined.
Return the cooled potatoes with celery and onion into the large serving bowl. Pour the dressing over the potatoes and gently stir with wooden spoon until the spuds are fully coated.
Cover with plastic wrap. Serve within 2 hours at room temperature. Or, refrigerate for up to 12 hours, or overnight. Best if allowed to return to room temperature before serving. Give the salad a few good mixes with the wooden spoon.
Garnish with a nice sprig of dill.