Place the anchovies into a blender or food processor. Throw in the Dijon mustard, vinegar, Worcestershire, garlic and lemon juice. Pulse the processor or blend on low speed for several seconds. Scrape down the sides.
With the food processor or blender on, drizzle the olive oil into the mixture in a small stream. Scrape down the sides.
Add the Parmesan, salt and a generous grind of black pepper. If you want to keep it strict orthodox “paleo” then forgo the parmesan.
Pulse the whole thing together and mix until thoroughly combined. Refrigerate the dressing for a few hours and allow the dressing to marry.