Our broker engine runs on a z/OS mainframe.
It processes requests from various clients and one of the clients is a webpage. For our applications on the web that use broker, we have 2 pieces of middleware to facilitate communication between the web and our mainframe - broker being one of them.
The question has arose, is it possible to shut down broker by pushing a ‘panic button’ and when the fear has passed, push another button to restart broker? Obviously this would need to be done in real time and on demand.
Is it possible to do this?

You can stop and start broker with z/OS operator commands. I assume that this is not the answer you are looking for. Could you please provide a little more detail about exactly what you want to do?

also, are you really looking to stop the server(s) rather than the Broker? Most “panic” issues are application issues (loops, memory leaks, CPU usage, excessive database calls, etc), so shutting down the Broker might not resolve them, where shutting down the servers is more likely to aid in resolving the problem.

There are different ways to stop the servers, depending on the platform they are running on. Using Broker administration (SMH) to deregister them is one option if the messaging side of the application is getting out of hand.