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