Begin by removing the tough outer leaves from a medium head of cabbage and cutting it in half. Finely slice each half into thin strips and transfer to a large mixing bowl.

Core the apples and slice them into quarters or dice them. Add apple pieces to the bowl with cabbage.

Toast walnuts in a medium pan with olive oil over medium heat for about 5 minutes. Roughly chop and fold into the salad, reserving some for garnish.

Combine dressing ingredients in a glass jar, secure the lid, and shake until emulsified.

Add half of the Parmesan cheese into the salad bowl, drizzle with dressing, and toss gently. Let it rest for at least 10 minutes before serving.