Place the potatoes in a large pot. Cover with water, bring to a boil, then cook at a medium boil until the potatoes are just tender when pierced with a fork, about 10 minutes.
Meanwhile, in a large bowl, combine the honey, mustard, salt, and vinegar, whisking to combine. Slowly drizzle in the olive oil, whisking again until well incorporated.
When the potatoes are cooked, drain and cool slightly. When cool enough to handle, slice into ½ inch slices.
Add the sliced, still warm potatoes to the oil and vinegar mixture along with the celery, dill, and green onions. Using a large spoon or your hands, toss everything together, being careful not to break up the potatoes too much.
Taste and add additional salt or vinegar if you like. Allow to sit to absorb the dressing, then serve warm or at room temperature.