Place the sliced celery in a medium bowl and sprinkle with the kosher salt. Massage the salt into the celery and let it sit for 30 minutes. Drain and discard any liquid that has collected and gently squeeze excess water from the celery. Pat the celery dry with a clean kitchen towel or paper towels, then set aside.
In a medium bowl, whisk together the white wine vinegar, olive oil, dill, parsley, caraway seeds, sugar, and black pepper. Adjust seasoning to taste.
Add the celery to the dressing and toss until evenly coated.
Cover and refrigerate for at least 1 hour, until chilled. Stir once more before serving. Serve cold. (The flavors continue to develop as the salad sits, so if you can make it the night before, even better.)