Place anchovies into a blender or food processor with garlic, Dijon mustard, Worcestershire and vinegar. Next, add lemon juice and blend well.
Pulse the processor or blend on low speed for several seconds. Scrape the sides. With the food processor or blender on, drizzle olive oil into the mixture in a small stream to emulsify. Scrape the sides, and mix again to thoroughly combine.
Add salt, black pepper and Parmesan cheese. Pulse the whole thing together and mix until thoroughly combined.
Refrigerate the dressing for a few hours before using it on the salad to combine the flavors.
Preheat grill to medium high.
Brush all romaine halves with olive oil on both sides and season with salt and pepper.
Place on grill and cook for 2-3 minutes per side, until nicely charred.
Place 2 cooked romaine halves one each plate and drizzle with dressing top with anchovies (optional), cheese and serve with a Skewered Mozzarella-Bagna Càuda on the side.