Place the anchovies, garlic and salt in a mixing bowl. Mash with a fork to make a paste.
To the mashed anchovies and garlic, add the pepper, egg yolks and Dijon mustard.
Using a wire whisk, mix everything together until creamy in texture.
With one hand, drizzle in the olive oil, drop by drop at first, while whisking with the other hand to form an emulsion.
Once your mixture is thick, pour the palm oil in a slow thin stream while continuing to whisk.
Add the lemon juice and stir until well blended.
Taste the dressing. Add more salt, pepper or lemon juice, as needed. You don't want it to be too tangy. You're aiming for creamy and a bit salty with a subtle but unmistakable tang.
Use your Caesar salad dressing on any vegetable salad. It's isn't just for Caesar salad, really. It's good for all kinds of vegetable salad.