Combine shredded green cabbage, red cabbage, and grated carrots in a large bowl. Sprinkle with fine salt and toss to coat. Set aside for 10 minutes.
Transfer the salted vegetables to a clean kitchen towel and squeeze firmly until no more liquid comes out.
In a separate bowl, whisk together mayonnaise, apple cider vinegar, sugar, Dijon mustard, celery seeds, and black pepper until smooth. Taste and adjust if needed — it should taste quite tangy at this stage.
Add the squeezed vegetables and sliced green onions to the dressing bowl. Toss thoroughly until every strand is coated.
Cover and refrigerate for at least 30 minutes. Taste once more, adjust seasoning, and serve.