Prepare the Cabbage: Remove outer leaves, cut in half, slice off core, and shred into thin strips. Place in a large salad bowl.

Slice the Apples: Cut apples into quarters, remove core, slice into 1/4-inch pieces, and add to the bowl with cabbage.

Toast the Nuts: In a skillet over medium heat, add olive oil and chopped walnuts. Toast for about 5 minutes until fragrant.

Make the Dressing: Combine olive oil, apple cider vinegar, honey, Dijon mustard, salt, and black pepper in a jar and shake or whisk until emulsified.

Assemble the Salad: Add half of the parmesan cheese and the dressing to the cabbage and apple mixture. Toss gently to coat.

Finish and Serve: Sprinkle reserved walnuts and remaining parmesan on top, then serve immediately.