Scrub the potatoes thoroughly and dice into uniform one-inch cubes.
Place potatoes in a large pot and cover with two inches of cold water.
Add two tablespoons of salt to the water to season the potatoes internally.
Boil over medium-high heat until fork-tender, roughly 12 to 15 minutes.
Drain in a colander and return to the warm pot for two minutes to evaporate excess moisture.
Whisk the mayonnaise, mustard, salt, and pepper in a medium bowl until smooth.
In a large bowl, combine the warm potatoes with the dressing, diced celery, minced onion, and chopped eggs.
Gently fold in the fresh dill until evenly coated.
Adjust salt and pepper to taste and serve chilled or at room temperature.