Start by mincing the garlic cloves finely.
In a medium mixing bowl, add the minced garlic, anchovy paste (if using), freshly cracked pepper, capers, lemon juice, and Dijon mustard. Whisk these ingredients together until well combined.
Add the mayonnaise to the bowl and mix thoroughly until the mixture is smooth.
Add the grated Parmesan cheese to the mixture and continue whisking until fully incorporated.
While whisking continuously, slowly drizzle in the extra virgin olive oil.
Taste your dressing and add salt as needed before serving.
You can serve the dressing immediately or transfer it to a storage container and refrigerate for later use.