In a jar with a lid, add the olive oil, balsamic, mustard, apple cider vinegar, and salt and shake vigorously to combine.
In a large mixing bowl or salad bowl (preferably a wide shallow bowl), add radicchio, arugula, and apples. Toss with ¾ of the dressing. Add more dressing, to taste.
Transfer the salad to a big platter (or keep it in your salad bowl), and top with the parmesan, walnuts, and black pepper.