Preheat the grill to medium high heat.

Brush the cut side of the lettuce with olive oil. Place on the grill, cut side down, until grill marks appear, about 3 minutes.

In a blender or food processor add the anchovies, garlic, egg yolks, mustard, and beer. Blend until well combined and light and frothy, about 3 minutes.

Heat the olive oil until hot but not smoking (20 seconds in a microwave is sufficient). While the food processor is running, slowly add the oil, drop by drop, until an emulsion forms. Add the salt, pepper, and Parmesan cheese, pulse to combine.

Place each Romaine half on a plate, drizzle with dressing, top with remaining Parmesan and croutons. Serve with knife and fork.