Great post, came home with Chicken Shawarma from Amir's (why Amir's doesn't have garlic sauce I don't know) and thought I have Zankou's sauce in the fridge, no problem!
Wrong, had about two teaspoons in a yellowing container way back in the slums of my fridge.
Panicked, I found your post and it set me off on my quest.
This is a good recipe and I'll use it in the future for dips and such, but this is not Zankou's, it's Toum with a starch extender added (I didn't know that until about two hours ago, started my search with your recipe and worked toward Zankou).
The Zankou recipe, as far as I can tell, is only Garlic, Salt, Lemon Juice and Oil, nothing more.
The trick is to mix it all up just right so that you get a heavy emulsion that gives you the thick consistency of Zankou's.
I knew very little about emulsions yesterday, if you don't I recommend spending a few minutes reading up, it's truly worth the time.
To get a good thick emulsion you need water, a "mortar" agent and lots of oil.
Garlic juice is a good emulsion agent, just as eggs are in mayonnaise, but the secret is to get the juice, to do that you need to either mash or press your garlic.
Throwing solid garlic into the blender will give you lots of flavor, but little binding activity, which is why the potatoes are needed for thickening.
Press most of your garlic and leave a few cloves whole.
Follow your recipe as described, adding the pressed garlic to lemon juice and salt.
Very slowly add a dribble of oil as the blender is running, once most of the oil is in, add the remaining whole garlic.
The pressed garlic will give you the emulsifying effect that will make the sauce very thick and the whole garlic will give it the grain of Zankou's.
If you add all of the garlic in the beginning you will get fantastic sauce, but the garlic will all be pulverized leaving a perfectly smooth sauce, but the flavor is unchanged.
My finished product is exactly the flavor and thickness of Zankou's, the only difference being that it is slightly lighter and fluffier than the original, but only a bit, I actually like it better.
I'm guessing that the difference has to do with the type of oil used, I used only Canola, Zankou probably uses a proprietary blend to get the heavier texture.
Just made this an hour ago, bet that after a day in the fridge it will be even closer to the original.