Remove the outer leaves of the cabbage, slice it in half, and cut off the core. Finely slice the remaining cabbage segments and place in a salad bowl.

Cut apples into quarters, remove the core, and slice about 1/4-inch thick or dice into cubes. Add to the bowl with the cabbage.

Toast walnuts in a skillet with olive oil for about 5 minutes until fragrant and golden brown. Cool slightly and chop before adding to salad.

Combine olive oil, vinegar, honey, mustard, salt, and pepper in a jar. Shake for 30 seconds until emulsified. This dressing elevates the salad.

Add half of the Parmesan cheese and the dressing to the salad bowl, toss gently, and let sit for 10 minutes before serving. Garnish with remaining walnuts and cheese.