Preheat your oven to 350°F (177°C). Spread the walnuts evenly on a baking sheet and roast them for about 10 minutes, or until they become fragrant and golden.

In a large mixing bowl, whisk together the Dijon mustard, ¼ cup of olive oil, 3 tablespoons of vinegar, 1 tablespoon of sugar, and half a diced onion until fully emulsified.

Using a mandolin or food processor, shred enough Brussels sprouts to fill about 4 cups. Combine with the coleslaw mix and sliced apple.

Pour the prepared dressing over the shredded mixture and toss everything together gently with tongs until fully coated.

Allow the mixed slaw to rest for 15-20 minutes at room temperature.

Just before serving, sprinkle the cooled, chopped walnuts and optionally grated Parmesan cheese over the salad.