Over at Sitepoint, Younes Rafie wrote a tutorial on how to create a custom mail driver in Laravel 5.3. In the post he shows some code that can log all email to the database.

One of the many goodies Laravel offers is mailing. You can easily configure and send emails through multiple popular services. ... Laravel also provides a good starting point for sending mails during the development phase using the log driver, and in production using smtp, sparkpost, mailgun, etc. This seems fine in most cases, but it can’t cover all the available services! In this tutorial, we’re going to learn how to extend the existing mail driver system to add our own.

https://www.sitepoint.com/mail-logging-in-laravel-5-3-extending-the-mail-driver/