There is no faster than light broadcast communication. I don't let ships move FTL through normal space, so I'm not letting energy do it either.
What does exist is a device called a message pod. It is a small (about the size of a German shepherd), unmanned craft complete with a gravity drive for movement through normal space, a small hyperdrive for crossing the distances between stars, and appropriate navigational systems. When you need to send a message to another solar system, you record it in the message pod, give it its destination, and launch it. It locates and flies to the lowest point in the local gravity gradient attainable within a preset period of time, then catapults itself to its destination where it delivers your message.
In the more developed areas of the galaxy, a system has been arranged to use message pods to simulate a form of broadcast communication. Fleets of pods are constantly in transit between pairs of stars. As soon as a pod arrives in system, it begins broadcasting all the messages it carries. At the same time and on a different frequency, it collects all the messages transmitted to it. Meanwhile, it makes the transit from the edge of the system where it arrived to the center of the system where the gravity well is deepest. Once it arrives there, it jumps to the system on the other end of its route and repeats the process. In theory, the pods are timed so that as soon as one leaves the system, another one arrives. In practice, the time variance of hyperspace ruins the effect. To compensate, pods are added to each route until a relatively constant coverage is achieved. Each pod stays in system for about a day at a time.
The pods talk to each other as well. Two pods in the same system trade information and deliver it back to their respective origins. In this way, a message can work its way across the web of comm routes to reach destinations far removed from a direct connection. This also provides redundancy and speeds the average time taken to deliver a particular message.
That is how the public communication system works. Messages can be sent encrypted, but they are still delivered to everyone within broadcast range of the pod. A more secure method is to hire a private message pod. With it, you have the option of telling it to seek out the target of your message and deliver it directly via a hard data line. This method is more secure, but it has its own problems. First, the pod must directly find the target of the message. It cannot rely on other pods to carry its message over a wide area. It alone must travel from system to system in search of its goal. Second, it is potentially slower, since it is working alone. Third, if something should happen to the pod, the message is lost entirely. There's no backup. Pods for hire have a policy of returning to their origin after delivery or after a set amount of time to report success or failure.
Combined, these two methods of public and private pods cover the majority of communication needs. However, starships can find themselves away from civilization where the pod net has yet to be established. For that reason, ships carry a supply of message pods with them for use when away from home. They are plentiful enough that ships aren't shy about using them for everyday communication, rather than saving them up for emergencies.
The design has been standardized over the centuries, and is compatible with just about any communications system in civilized space. They are protected from harm by treaty, under threat of the offender being excluded from the network if breached. Using them for target practice is right out. Due to their superior power to mass ratio, they are able to hypertransit faster than a manned ship attempting the same passage. They are highly maneuverable and yield right of way to any approaching object.