Make the garlic paste: On a cutting board, finely mince the garlic and anchovy fillets. Add the salt and, using the flat side of your knife, mash the mixture into a smooth paste. Transfer to a small bowl.
Whisk the dressing: Add the mayonnaise, Dijon mustard, lemon juice, black pepper, extra virgin olive oil, and Parmesan cheese to the bowl. Whisk until smooth and creamy.
Serve or store: Use immediately or transfer to an airtight container and refrigerate until ready to serve.