Place the potatoes in a medium stock pot and cover with 8 cups of water, making sure there’s at least 2” to the top. Add 1 TBSP salt and bring to a boil. Reduce heat to medium and simmer for 15-20 minutes until they a knife is easily inserted but not mushy.
Drain potatoes and return to the pan. Partially cover and allow to cool.
While the potatoes are cooling, chop the onions and celery and place in a large bowl (large enough to add the potatoes and have room to toss).
Whisk the mayonnaise, mustard, vinegar, 1 tsp salt, pepper and dill together to make dressing.
Add the potatoes to the onion and celery. They should be warm, but not hot.
Add the dressing and toss to blend.
Take a large chef’s knife and run through the potatoes to break them up a bit.
Refrigerate until ready to serve, at least 1 hour.