I keep seeing lines like this in the LISTSERV log:

1 Mar 2018 09:31:48 Processing file 3215 from MAILER@LISTSERV.EXAMPLE.ORG

-> New subscriber, will process in 10 minutes.

What in the world is this?

LISTSERV has a feature called "spam quarantine". This feature holds all messages from non-subscribers and the first message from new subscribers for 10 minutes (the default) to help compensate for network latency that could result in a spam alert not reaching your machine until after the spam in question has been distributed to your list(s). You can adjust this (or defeat it completely) either at the server level (with SPAM_DELAY= in the site configuration) or at the list level (see the Spam-Delay(n) parameter of the Loopcheck= list header keyword).

The purpose of holding the first message from a new subscriber to a given list is to help avoid situations where a spammer subscribes to a list, posts, and then unsubscribes in order to get around Send= Private.