Bill:

This might be right.

3 garlic cloves
1 half tin anchovies (about 6 filets) in olive oil, drained
Juice of 2 lemons
2 tablespoons dijon mustard
2 tablespoons red wine vinegar
1 hard boiled egg
1/4 cup shredded parmesan cheese
1/2 teaspoon worcestershire sauce
1/4 cup olive oil

Blend all except the olive oil above in a blender, food
processor, or with a stick blender.  Drizzle in the olive oil
slowly as you blend more so it emulsifies.

But see also 

Caesar Salad and Pesto
Cilantro Lime Caesar
Another Mexican Caesar