These steps allow you to create an announce-only mailman list. That's a mailman list that you do not wish to have discussions on. All posts will need to be approved by the moderator.
1. In cPanel, go to Mailing Lists, select your list and select the Manage link.
2. Go to Membership Management.. and set the moderation bit for all users. The option is at the bottom and says "Set everyone's moderation bit, including those members not currently visible".
3. Go to Privacy Options » Sender Filters and set the option "By default, should new list member postings be moderated?" to "Yes"
While it's not strictly necessary, you probably also wish to set the Reply-To headers, like this: