When you really want your umami, there's no substitute for this.
2 heads romaine lettuce, limp outer leaves removed
1/3 cup Parmigiano-Reggiano cheese
1/3 virgin olive oil (or extra virgin olive oil)
1 tsp. Worcestershire sauce
3 tbsp. lemon juice
1 large clove garlic
½ tsp. pepper
1 tsp. capers
1 tsp. brown mustard seed
a pinch of sea salt
Step 1: Coddle the egg
Bring a small saucepot of water to a rolling boil. Immerse the egg in the water for 45 seconds, holding it in a slotted spoon. Place the egg in the refrigerator until ready for use.
Step 2: Assemble the dry spice base
In mortar and pestle, grind the pepper and mustard. Thoroughly crush the garlic clove under the flat of a knife. Add salt, pepper, and crushed garlic to mustard powder.
Step 3: Prepare the liquid ingredients
Finely dice the anchovies and capers. In mixing bowl, combine the lemon juice, Worcestershire sauce, diced anchovy, and diced caper. Mix well. Separate the yolk out from the coddled egg. Thoroughly mix all liquid ingredients until smooth using a wire or silicone whisk, then whisk in dry spice base.
Step 4: Whisk!
Very slowly -- about an ounce at a time -- pour in the olive oil. Whisk continuously while the oil is poured in until it combines before adding more oil. Ideally, the pour of oil is very slow and continuous during vigorous whisking. After all the olive oil is added to the dressing, then whisk in grated cheese.
Step 5: Adorn
Chop the lettuce into medium-sized chunks, separating out the cores. Drizzle the dressing on the lettuce and toss. If desired, shave additional cheese or add additional whole anchovies to dressed salad.
Coddling the egg first produces a creamier, better-mixed dressing than a raw egg yolk. You will not use the albumen of the coddled egg but may retain it for use in some other dish (say, a quiche or a pie) if you wish; refrigerate it promptly.
If the idea of eating an anchovy repels you as it does many Americans, my first reaction is, "get over it," because what most people dislike about anchovies is their texture, and you should be chopping these little fishies almost into a paste. But if that is not enough to induce you to deal with the mere presence of the delicious fish, then you can swap out more capers for the anchovies. Doing so renders the salad truly vegetarian. I know of no substitute for Parmigiano-Reggiano which would then render the salad vegan -- and I can tell you that tofu won't do it because it's mainly protein and the cheese has a high fat content.
The original Caesar salad was invented by Caesar Cardini, a famous Italian immigrant who became a restaurateur in California during the early days of Hollywood. Cardini moved his restaurants from Los Angeles and San Diego to Tijuana, Mexico during prohibition, and the Cardini's restaurants, featuring Cardini's signature salad, became one of Tijuana's high-end tourist attractions during this time. His waiters would develop an elaborate show of making the dressing while telling jokes or describing their activities, particularly while pouring in the oil into the mixing bowl from a great height with one hand and whisking with the other. When you make the original Caesar salad as I've described here, you're re-creating a bit of Hollywood's golden age in addition to making a much, much better dressing for your salad than anything you could possibly buy in a bottle.