I’ve tried a few different cold brewing methods - French press, cheesecloth bag, pouring through a paper filter - and finally found one I like that is minimally messy. (As @Saregama noted, it’s not really possibly to be unmessy.)
County Line Kitchen - Cold Brew Mason Jar iced Coffee Maker, Durable Glass, Heavy Duty Stainless Steel Filter, Flip Cap Lid - 64 oz (2 Quart / 1.9 Liter), With Handle https://a.co/d/gZuJCkV
This has a stainless steel insert for the grounds… after brewing, just lift it out and dump the grounds into the trash (or compost). It is SO much easier to clean up than the other methods I’ve tried.
I use 8 scoops of beans, ground medium-coarse. (For comparison, I’d use 2 scoops of beans ground fine for 12oz water if I make pour-over.) I have the 64oz jar but with the grounds in the filter, I can generally only get about 6.5 C water into the jar. I let it brew in the fridge for 18-24 hours. I mix the concentrate about 1:1 with milk, no ice.