A321 Captain reported Number 2 Engine Vibration in climb. The flight crew ran the QRH and checklists; and retarded the Number 2 Throttle to idle. The flight crew requested priority handling and performed an air turn back and precautionary landing at departure airport with the Number 2 Engine Throttle at idle.

Narrative

During climb; between ZZZZZ and ZZZZZ1 fixes on the ZZZZZ1.2 departure; thrust levers were at climb and speed and climb were managed. At approximates FL227; we encountered an Excessive Aircraft Vibration event. We requested a level off with ATC and began to troubleshoot.The F/CTL page displayed no control surface fluttering so we moved onto the Engine page. We noted that Engine 2 in comparison to Engine 1 had a much higher level of Engine Vibration. The indication was not amber or red and its reading was 2.1-2.4 which; honestly; is a not an uncommon reading.I suggest to the First Officer (FO) who was acting as PF (pilot flying) to reduce the #2 Thrust Lever to idle. Once the engine speed was reduced the vibration ceased. I then suggested to the FO that he try to slowly increase the TL (thrust lever) back towards the climb detent. He was unable to make it more than halfway to the CL detent and the vibration returned. So; we elected to leave the #2 Engine at idle. We choose not to shut down the #2 Engine as we were still able to utilize the Engine Driven Generator; the Yellow Hydraulic Engine Driven Pump and the #2 Engine Bleed Air System; not to mention should we need the engine; although we would have expected vibration; at least we would have had it available. We also decided to start the APU and utilize the APU Bleed Air; below 10;000 ft.; this way if we had to go around; we would have max thrust for the go-around as we had planned to only utilize the #1 Engine for the go-around should we need to perform one.For your timing most of what happened in the prior paragraph was most likely less than a few minutes of discussion. We were still level at about FL230; the Flight Attendants were calling in a mild state of panic regarding the vibrations and I told them to Standby.We divided duties at this point. I had the FO [request priority handling] and request vectors back to ZZZ and prepare the FMGC for a return to field.I contacted Dispatch to advise of the return to field and the nature of the mechanical abnormality. The Crew Phone was not able to function properly; which in hindsight I felt like I wasted a bit too much time focusing on trying to make a call to the Dispatcher rather than just using the ACARS. I advised the Flight Attendants of a precautionary landing; to include a brief description of the situation and to reassure them that we had total control over the aircraft. I told them that we had about 20-30 minutes to land. After speaking with the Flight Attendants; I made a general announcement to the Passengers essentially detailing that the aircraft was fine and as a precaution we were returning to ZZZ to have our maintenance team inspect for any issues.By the time I returned to rejoin with the FO we were now about at 11;000 ft. and about 30 miles from ZZZ. He briefed me on the state of the flight and we went through the overweight landing QRH procedures and performed the landing assessment. We didn't utilize the non-normal landing checklist in the OD pages of the QRH. Passing 10;000 ft. we gave the Flight Attendants prepare for landing PA and the sterile chime. Almost simultaneously; and just as we were about to conduct the descent checklist; we got an AIR ENG 1 Bleed Fault ECAM; which again; in hindsight; most likely correlated with my turning on the APU Bleed. We asked for extended vectors to accomplish this additional ECAM procedure.Once the ECAM actions were completed and we ensured no critical follow up items were to be performed; (it appeared there was only the possibility of a computer reset so we elected to forego that procure.) We briefed the visual approach to XXR; which was a requested ATC runway change; and conducted the descent checklist.From here on it was an uneventful approach and landing albeit overweight. The FO did have to use manual thrust control because we didn't have the #2 Engine Shutdown and so Auto Thrust wasn't available. And actually; now that I think about it; after our initial level off at 11;000 ft.; our speed did get quite slow for a moment; never below Vls but headed that was in a hurry. I'm not sure if the FO momentarily forgot that auto thrust wasn't on anymore or was just a bit too slow to introduce thrust to arrest the speed decay but as the Autopilot began to level off; we began to slow quite rapidly. I prompted him to add power almost exactly as he was already doing it. After that there were no more slow speed issues as we were both acutely aware of the manual thrust situation. We flew in for the visual approach to Runway XXR in ZZZ. We had Airport Rescue and Firefighting (ARFF) standing by and after landing we stopped on the runway for a visual inspection and a thermal reading of the brakes. After ARFF responded that they saw nothing abnormal and I felt we had positive control of the aircraft on the ground for taxi operations; I elected to taxi the aircraft to the gate with ARFF following.Once at the gate we had the Passengers remain seated just until we had a game plan from Maintenance and operations and in less than five minutes the Passengers were instructed to deplane as the aircraft was taken out of service. While deplaning Maintenance was hovering in the flight deck doorway asking lots of questions it was a bit unnerving as both my FO and I were really starting to feel the effects of the adrenaline rush starting to fade. Anyway; I made three logbook entries. 1. Regarding the Vibration which I tried to convey that the Vibration was the complete aircraft vibrating and that the Vibration was only resolved by reducing the power on the Number 2 Engine. 2. I wrote up the ECAM for the AIR ENG 1 Bleed Fault. 3. I wrote up the overweight landing and noted that it was a smooth touchdown.Once that was done I received a Dispatch message via ACARS asking me to call. I called and we just discussed in cursory detail what had happened.Next the Chief Pilot Name called and asked if the FO and I were okay and that she was going to pull us off our sequence to get a chance to unwind.Lastly; and I wish it was firstly; I had a chance to say goodbye to the remaining Passengers and apologize for the delay to their travel; but most importantly I was able to make sure that the Flight Attendants were okay. I also discussed with them how they felt the situation went. They liked that when they initially called; I told them to 'Standby'. They explained to me that just hearing 'Standby' gave them peace that at least we knew something was wrong and that we were most likely trying to solve it. I can only imagine that they would be fearful of their calls not being answered at all. Secondly they explained that when I called them back to advise them of a precautionary landing that I also advised them that we had complete control of the aircraft.As I don't know how the vibration propagated I have no answer as to what may have caused the vibration.I only have some hind sight suggestion regarding a vibration event. I'm sitting here in front of my PC nearly 24 hours from the incident. I've been watching the electronic logbook to see what the corrective action take is because I'd like to know more about the why this happened. I want to make sure I could have avoided this situation in the first place. Sadly the aircraft was signed off as 'checked vibration within limits'. Since its sign off the aircraft has been refused by two crews already.My point for a corrective action may be in how we record in the logbook and engine vibration vs an airframe vibration. At a minimum this airplane should have been test flown prior to return to service. So to simplify my long winded answer to this important question. Have a method of reporting vibration that triggers a test flight prior to return to service or require any vibration to be test flown prior to return to service.