Secure Broadcast Channel
The problem is not broadcast, but secure broadcast. Secure broadcast guarantees that every recipient ends up with the same message.

If you just sign the message and send it separately to each recipient, a malicious sender could send different messages to different recipients.

A simple solution is that each recipient counter-signs the message and re-sends it to the other recipients. Once everyone has everyone's signature on the message, they accept.

There are better solutions, but all of them have an associated cost.