We do not recommend using the Mailing List tool in cPanel, because that tool cannot throttle.
To send more than 500 emails, you must use a mailing program which can throttle emails, so we recommend phpList found in Fantastico Deluxe.
Read how to use PHPlist and throttle email.
There is also a limit to the number of Mailman mailing lists permitted as follows (NOTE: This does not apply to other mailing list programs such as PHPList. This only applies to Mailman.
* Hatchling package: 20 Mailman mailing lists
* Baby package: 25 Mailman mailing lists
* Business package: 50 Mailman mailing lists
* Reseller and Dedicated packages: Unlimited number of Mailman mailing lists
Mail Man lists can be used by going to cPanel > Mailing List and following the setup.