You can prepare this dressing by hand with a whisk and some elbow grease, but it's easier to use a blender or food processor.
Put all ingredients except oils and parmesan in bowl of food processor or blender (or in a bowl) and combine well.
With food processor (or blender) running, slowly dribble in oils--or slowly whisk in oils, if making by hand.
You could use either all olive oil or all canola oil, but I prefer to use both.
Lastly, blend in the parmesan.
Taste; adjust seasonings as you wish (you may want to add salt, but the anchovy paste and worcestershire do provide the recipe with a fair amount of saltiness).
Either use right away, or refrigerate; it thickens when chilled, however, so you may have to give it a little whisk to loosen it up if you've stashed it in the fridge (it makes a great dip when thickened, though).
This dressing makes enough to dress one large caesar salad.