In a mixing cup, combine the anchovy paste, minced garlic, lemon juice, Dijon mustard, Worcestershire sauce, mayonnaise, and oil. Whisk until smooth and add the 2 tablespoons of grated Parmesan and a few turns of fresh cracked black pepper.
Add broccoli slaw and mixed cabbage to a large mixing bowl and pour dressing over the top. Toss well to combine and let sit for at least 20 minutes or up to four hours in the refrigerator. This will help to breakdown the broccoli and cabbage and make it more tender.
Dressing can be made 1-2 days ahead and refrigerated.