Easy cold-brew coffee with a French press

I disagree with using a French press for cold brew for it does not properly filter the grounds for me. I prefer using a glass vessel with a rubber top, placing the grounds inside with filtered water and leaving in the fridge for 8-12 hours. Then, I filter that through two mesh filters (fine and standard tea style) collecting most (if not, all) of the grind and “silt”. Yes, it’s not as simple as using a French press but I think quality is more important to me than ease of use concerning cold brew coffee.
French pressing for cold brew would seem more optimal if you’re camping or traveling, in my opinion.