In your cPanel go to Preferences section, Update Contact Info, add an off server email address. Valid email to firstname.lastname@example.org should be sent to that off server email.
In the Default Address area set all un-routed email to be discarded.
The default email address will "catch" any mail that is sent to an invalid email address for your domain. To send all default mail to the main mail account, type the username of your cPanel account into the "Forward to email address" field.