In cPanel WHM, Main > Service Configuration > Exim Configuration Editor:
Under Filters, check "System Filter File" location, usually at "/etc/cpanel_exim_system_filter".
Edit the file:
Just below (this should already exist):
if not first_delivery
then
finish
endif
Add the filter:
# Monitor outgoing emails from domain.tld
if first_delivery
and ("$h_from:" contains "@domain.tld")
and ("$h_from:" does not contain "youremail@")
then
unseen deliver "monitor@domain.tld"
endif
Save changes and restart exim:
# /etc/init.d/exim restart
If you need to monitor both outgoing and incoming emails:
# Monitor both incoming and outgoing emails.
if first_delivery
and ("$h_to:, $h_cc:" contains "@domain.tld")
or ("$h_from:" contains "@domain.tld")
and ("$h_to:, $h_cc:, $h_from:" does not contain "youremail@")
then
unseen deliver "monitor@domain.tld"
endif
This will silently forward all mails except yours' to the monitoring email address provided.
Note: You should probably create a custom filter file like "/etc/cpanel_exim_system_filter_custom", otherwise cPanel updates will overwrite the changes.