B737 Captain reported at push back with engines running; ramp personnel approached; opened cargo door and loaded a box without permission; resulting in immediate shutdown of engines.

Narrative

Initially our pushback and engine start were normal. Pushback crew was cleared to disconnect the headset and I was given a salute. The pushback crew disconnected the tug; walked away from the aircraft; and the tug backed away towards the terminal. Shortly afterwards; one of the ramp personnel started walking towards the aircraft with a large box with the obvious intent to put it on our aircraft. We had just finished starting the #2 engine and were in the process of starting the #1 engine. This was a delayed flight (by over an hour) and I did not intend to further delay the flight to accommodate this one box that had just arrived. Initially; the lead marshaller signaled the ramper with the box to not approach the aircraft but this individual was intent on placing this on the aircraft and continued to approach the aircraft. The lead marshaller grabbed a headset and approached the aircraft; and it appeared to us that his intent was to contact us on the interphone and ask if we could take the package. At this point we still had the #2 engine running. To our amazement; they opened the cargo door and placed the box on the aircraft without having received permission from me to do so and without communication or coordination. We could not ascertain the location of the ground crew and I immediately shut down the #2 engine until the cargo door was again closed and the ramp crew walked away. At this point we restarted the engine and continued.I should mention that we had an FAA inspector on the flight deck on our jump seat and he observed this entire event. Person A intends to also file the equivalent form with the FAA (equivalent to our report form). This was a very surprising event as our ground crews are generally very well trained and would know not to approach the aircraft under these conditions. In my time at company I have never observed something like this.