@Snapey My UserRegisteredNotification is called as a class like this:
$user->notify(new UserRegisteredNotification($user, $this->reset_token));
Notice that the reference to the user is inside the calling class and if you don't pass it in, then you have to get the reference some other way. This appears to be how it's done in the Laravel docs too. In my notification class, I'm actually using the user object to print details in the e-mail. I just didn't post the code because it wasn't relevant to the problem.
Thanks again for the help.