Kirk gets bored during an especially long, uneventful journey/travel time thingy, and decides to play crew matchmaker, starting with Sulu and Chekhov.  Somewhere along the line, he falls for Spock.

'Verse doesn't matter so much.  If TOS, bonus points for utilizing the yeoman-backrub scene in Kirk's attempt to woo his First Officer.  If Abrmas'-verse, bonus points for Kirk's lack of verbal filter, blue jeans on the bridge, and making Spock curse, out in public as well as behind closed doors.

General bonus points if various members of the crew get caught pairing off in public places, Sarek expresses disapproval, and some sort of important transmission interrupts things.

Extra special bonus cookies if Kirk sings "Matchmaker" from Fiddler On The Roof, and at least one crew member asks him to stop or calls McCoy up to hypo him into submission.

I'd write it, but I think I'd kill it.