Hi Brent,
Hm, currently we do not have such feature to moderate only on first post on each blogger. However you can try to follow the steps below in order to make this possible.
1) Create another user group called "newly registered" from your joomla user menu,
http://screencast.com/t/LCmJbjLsLHg
2) Go to user options at your backend > global configuration > users and then set new user registration group to "newly registered",
http://screencast.com/t/WbWdeVsa . After that go your global configuration > permission tab > newly registered and set Site login to "allowed",
http://screencast.com/t/oPohOUTU .
3) Next go to your backend > easyblog > ACL > newly registered and set allowed to publish blog post to "No",
http://screencast.com/t/HeKvD6glH . Set the rest of ACL permission accordingly.
4) When a new user is registered on your site they will be automatically registered under "newly registered" user group and when they are trying to post a blog post, the blog will then go into moderation state where you can access it from your backend > easyblog > post > pending.
5) When everything is check out, publish the blog post and then look for the user that publishing the blog post inside backend > easyblog > authors and then edit the user user group to normal registered user so they will then have the privilege to publish a blog post without moderation,
http://screencast.com/t/27JAK9kqIh9 .
Hope these help.