Remove the outer leaves of the Romaine heads, separate the remaining leaves and wash to remove all the grit. Cut into small pieces and reserve.
In a non-reactive salad bowl, mash the anchovies and garlic together. Add the dry mustard and the Worcestershire sauce, mixing well. Incorporate the lemon juice and slowly pour in the olive oil until an emulsion forms. Toss the romaine lettuce in the dressing adding the grated Parmesan a third at time. Serve.