Well, this one had me baffled for a while. I thought that the user had to exist before I could send emails "from" that address.
But that makes no sense if I were to ignore all emails from email@example.com.
So, I did a little research and discovered that it's a CPanel setting!
Log into your CPanel and go to "Email" > "Set default address".
You can choose to forward the email to a valid address, but in the case of a "no-reply", just discard it by selecting "Discard (Not Recommended)".
Click "Change" to save.