I can personally attest to the authenicity of this recipe having had it made in front of me at Cardini's in Mexico City many moons ago. The recipe comes from Julia and Jacques Cooking at Home. Here are the notes that accompany it:
"When Caesar Cardini first served his famous salad in the early 1920s, he used just the hearts of the romaine lettuce, the tender short leaves in the center, and he presented them whole. The salad was tossed and dressed, then arranged on each plate so that you could pick up a leaf by its short end and chew it down bit by bit, then pick up another. However, many customers didn't like to get their fingers covered with egg-and-cheese-and-garlic dressing, and he changed to the conventional torn leaf. Too bad, since the salad lost much of its individuality and drama. You can certainly serve it the original way at home — just provide your guests with plenty of big paper napkins. And plan to be extravagant."