Combine the mayonnaise, anchovy paste, capers, parsley, lemon zest and garlic. Whisk in the red wine vinegar, lemon juice and season with salt and pepper. Add more or less red wine vinegar and lemon juice depending on your preference of acidity and consistency of the dressing. If you prefer the dressing to be looser but less acidic, use water instead of vinegar.
I used whole anchovies instead of anchovy paste. I also went lighter on the lemon juice.