I brew my cowboy coffee with a very fine Turkish Grind. The video has been posted here before but for me, it's key to bring the water to a boil, add the grinds, return it to a boil, and then remove from heat. If you YouTube "Turkish Coffee", this technique seems to be pretty standard. Greek Coffee is pretty much the same thing but I believe that they boil it three times.
The grinds (again, Turkish ground) settle to the bottom of the mug and don't bother me. This is what coffee is like through much of Eastern Europe and it's in my opinion far superior to Starbucks.
I'm now playing around with cold-brew coffee (toddy). I tried it earlier this week and it shows promise for the backcountry. I threw the grounds (coarse grind) in 16oz of cold water before going to sleep. It's pretty easy to keep 95% of the grounds out of your mug the following morning by being careful when you pour but a bandana or equivalent would work to filter out the remaining grounds. The grinds don't bother me so I didn't bother. You'd then simply heat the coffee to your temperature preference.
The flavor is different than cowboy/Turkish coffee but not objectionable. I haven’t decided which I like better but the cold brew is the easiest (not that cowboy/Turkish coffee is all that difficult). Still better than the instant coffees I've tried.