Place the sauerkraut in a colander and rinse thoroughly under cold running water. Press gently to remove excess liquid and let drain completely for about 10 minutes.
While the sauerkraut drains, core the apple and slice it into thin, matchstick-sized pieces.
Peel and julienne the carrot into thin strips or grate it with a box grater.
Peel and finely chop the red onion.
In a small bowl, whisk together the mustard and apple cider vinegar until smooth. Slowly drizzle in the olive oil while continuously whisking. Add the honey, salt, pepper, and caraway seeds if using, whisking until well combined.
In a large mixing bowl, combine the drained sauerkraut, apple slices, julienned carrots, chopped red onion, and fresh dill if using.
Pour the dressing over the salad ingredients and toss gently until everything is evenly coated. Taste and adjust seasoning if necessary.
Cover the bowl and refrigerate for at least 30 minutes (or up to 24 hours) to allow the flavors to meld.
Before serving, give the salad another gentle toss, sprinkle with sunflower seeds if desired, and serve chilled.
