As a professional Barista, I state from experience that this recipe can easily be simplified, with the same smooth-taste results---USE A FRENCH PRESS, plain and simple. No filtering/re-filtering necessary. Just add freshly ground coffee, fill with filtered room temperature water, stir, put on the lid, stash in the fridge for 20 hrs., or on the counter for 12 hrs. When time's up, press down the lid pump, and you're left with a great cup of cold java; without hassle. And it's a wonderful added touch to save any leftover black coffee and freeze into ice cubes for the next day!!
I have a Toddy coffee maker, which cuts all the hassle of the straining as it has filters and a carafe for straining and storing. I've been drinking this for many years. You never see that slick oil on the top and the coffee is smooth. Love cold brew.