Already some good "nominations". Dozens more to come, probably.
Want to jump on @slaw ’s mention of Nels Cline. I don’t care much for his work with The Nels Cline Singers or Julian Lange BUT if he only played one solo and not another lick ever again, his solo in One Wing is all you need to hear. Tried to find a live non-concert version I’d seen but could not. This track off the album will have to do. That solo begins at 1:52 here...
https://www.youtube.com/watch?v=bF3pBjPwgtg
If One Wing didn’t convince, try his lengthier solo-ing in Impossible Germany from Sky Blue Sky (though I prefer the stripped down minimalist sensibility of that in One Wing).
https://www.youtube.com/watch?v=r_0BPqWpM_M
Thanks to Pokey77 for turning me on to Nels in what seems an improbable role in Wilco given Nels’ prior and on-going work in jazz.
I’ll leave one more (for now)...
Can’t pass up an opportunity to mention Neil Finn as a fantastically gifted song-writer who is blessed as few are with the gift of melody.
Taking a tip from Slaw, I too reserve the right to future contributions.