I recently received a new device for making cold brew coffee. It put out a really good cold brew. The filter is made out of a fine nylon mesh.
How coarsely (or finely) should the coffee be ground for best cold-brew extraction?
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Two guides do have specific (though differing!) recommendations on coarseness of grind for cold brew.
Personally, I use the latter because I find the filtering goes more easily with a coarser grind; see also this question about making cold brew easier to filter.
In addition to the above listed guides I have also found another two to answer your question.
Prima Coffee recommends a medium to fine grind. They are using an AeroPress with 2 filters. They do suggest that at least one of those filters are paper.
ChestBrew has a how-to video that demonstrates the process of making cold brew from start to finish. Their whole bean coffee packaging suggests a medium coarse grind.
My husband and I are huge cold brew coffee fans and we prefer the second option because we've found that too fine a grind makes the coffee taste burnt and too harsh a grind makes the coffee too bitter. The medium coarse seems to make it just right. However, we use a pitcher and a milk bag to make our cold brew which I feel may make a difference in overall taste as compared to the device you referenced in your question.
Hope this helps and good luck!