If you do not have an immersion blender, you can whisk the anchovy paste, egg yolks, lemon juice, and mustard together in a large bowl. Gradually whisk in the oil, and continue whisking until thick and creamy.
Mayonnaise can be made in a blender, so I am guessing that Caesar Salad Dressing can be as well…although I have never tried it myself.
This dressing can be made a day ahead of time if needed.
Anchovies are salty, so be careful with your initial addition of salt. Add a pinch at a time until the flavor is to your liking.
If you are nervous about consuming raw eggs, purchase pasteurized eggs.
Infants, pregnant women, older adults and other high-risk groups should avoid eating raw eggs.