PC-12 air ambulance pilot reported a ground collision with a golf cart on the ramp due to aircraft movement after the pilot set the parking brake and while shutting down the engine. The ground crew attempted to alert the pilot of the aircraft movement but the pilot was unaware of the movement or ground crew warnings.

Narrative

The flight originated out of ZZZ2 at XA:58 using IFR rules for the flight. And then headed to ZZZ1 to get the patient. The first leg of the flight went without any issues. The patient leg of the mission departed out of ZZZ1 using IFR. I had to takeoff using VFR rules and get my IFR clearance in flight. This leg of the mission took approximately 45 minutes to get to ZZZ. Upon arriving I flew the RNAV XX approach into ZZZ. After landing; I performed a 180 on the runway and taxied towards the ramp via Taxiway 1. I taxied directly down Taxiway 1 and crossed Runway XY and then turned left on Taxiway 2. Upon finding my turn off of the taxiway. I followed the 'follow me' golf cart into the parking area where I maneuvered around a parked Cessna caravan and a government owned Blackhawk helicopter. The marshaller guided me into the parking spot and all was without issue up to this point. I set the parking brake and started shutting down the aircraft as per the checklist. Myself; nor anyone else on the airplane realized we were even moving. While in the shutdown process; as I was about to pull the condition lever to the idle shut off position. I heard a loud band; and then the airplane seemed to move sideways and I immediately shutdown the aircraft. After shutting down the aircraft; I immediately asked if everyone was alright inside the aircraft. Everyone responded that they were alright. At that point; I opened the door of the aircraft and immediately started asking if everyone in the ground crew was alright. They all responded that they were ok. The marshaller then told me that I was rolling and he was not able to get my attention before colliding with golf cart. It was then that I realized that the aircraft was approximately10 feet forward of where I was originally parked and turned to the right. Immediately after the realization that the aircraft was not in the spot where I stopped. Immediately; I went into the aircraft and denoted that the parking brake was still set. And documented with imagery on the pilot crew telephone.Suggestions: Remove golf carts from the ramp / taxi area when no in use