A321 Captain reported the aircraft rolled uncommanded at the gate after the parking brake was set. Captain applied brakes to stop.

Narrative

On Day 0; flt ABCD; ZZZ1-ZZZ; after landing in ZZZ; as PF; I taxied Aircraft X into gate XX. After stopping; I set the parking brake; checked to make sure the accumulator had pressure; then looked to make sure parking brake" was shown on the display panel. At this time; I proceeded to shut down engine one; then engine two. Just as I started to shut down number two; there was a brief ecam; that we think said something about the parking brake. It was only on for about 1 to 2 seconds; then extinguished. Very quick. During this time; while the number two engine was spooling down; my FO noticed the plane started to roll forward very slowly; he said brakes brakes! Luckily my feet were still very close to the brake pedals. I applied the brakes to stop the slow roll. While still holding the brakes with my feet; I recycled the parking brake by turning it off; then back on again. After doing so; all indications showed that the parking brake was indeed set again. Not trusting the system now; I kept my feet on the brakes until the engines were totally spooled down; and the signal was given from the ground crew that the chocks were set. I then released the brakes; with no further incident. After the jetway was connected; I checked with all ground personnel to make sure there were no injuries or any damage. There were none. They informed us that the plane rolled forward approximately 3 feet. We were very fortunate. Upon speaking with maintenance there; he informed me that this exact aircraft; Aircraft X; had this same problem a few weeks earlier; was inspected then; found no problems; and was returned to service.There were no listed write ups in the logbook that I noticed during my initial pre-flight."