Cook potatoes in lightly salted water until a paring knife with pass all the way through easily. Drain. You'll assemble the salad while the potatoes are still warm.
While the potatoes cook stir the dressing ingredients together. Taste and adjust seasoning if needed. Potatoes are bland, so the dressing should be highly seasoned.
Combine the potatoes, celery, scallions and ham. Add the dressing and toss well. Top with paprika, parsley, and/or scallions if you like. Serve chilled.