Running a Linux CentOS server, it's one purpose in life is to serve CF11, which it generally does very well. But last week "Java" was killed by the oom-killer, and the process that triggered it was "C2 CompilerThre":

C2 CompilerThre invoked oom-killer: gfp_mask=0x280da, order=0, oom_score_adj=0

This shows Java being killed in the logs:

Out of memory: Kill process 73217 (java) score 733 or sacrifice child
Killed process 73217 (java), UID 48, total-vm:12282868kB, anon-rss:6391832kB, file-rss:0kB, shmem-rss:0kB

Can anyone shed any light on how the C2 Compiler is related to excuting CFML code, and if there's anyway I can work out exactly what it was up to?

I don't know anything at all about your error, sorry. if you're going to pay someone - I can suggest Charlie, he has does diagnosis / tuning (and cfml support if you need ever need it). He does support in 15m chunks, too. So if you're problem is is fixed in 5 minutes - you're not footing a bill beyond the "next" 15m marker. And of course reach out to him, first, and he'll et you know if it something he can help with before you even strat getting charged.