Add the garlic, vinegar and dijon to the blender and blend until the garlic is chopped.
Add mayonnaise and blend for about 10 seconds. With the blender running, drizzle the olive oil through the opening in the top of the blender and blend until thick and creamy. (Note: food processors also have small "drip openings" in the top for oil to be added slowly to create emulsions.)
Add the salt and lemon zest. Cut the lemon in half and squeeze the juice of half the lemon (about 1 1/2 tablespoons) into the dressing. Add the anchovies and blend until anchovies have completely dissolved and dressing is thick and creamy.
Taste for seasoning and add additional salt or cracked pepper if desired.