A Citation pilot reported they failed to maintain the proper speed during climb resulting in a stall and temporary loss of control.

Narrative

Departed ZZZ with 4 passengers and 2 pilots. MTOW was 15900. We took off on the ZZZ departure following radar vectors to join a fix in our flight plan. I opted to climb in vertical speed instead of indicated airspeed as I always do. My thought process was to smooth out our climb with a shallower climb for passenger comfort because we were receiving small altitude clearances as we were passed from controllers. We were cleared to flight level 340 and everything was doing good. Engines were set to correct power settings and we were maintaining good climb speeds. At flight level 330 made the 1000 to go call. Somewhere around 400 foot to go Autopilot did a hard right rollover and disconnected. I immediately corrected; left wings level and pushed nose over. We entered a left turning spin and my copilot and I reduced throttles; used rudders to stop spin; and slowly applied back pressure to recover level flight and introduce the power back to the engines to maintain level flight. Not knowing what had happened we requested priority handling and asked for nearest airport which was ZZZ1 but we opted to return to ZZZ feeling we had good control of aircraft and wanted to stay out of busy airspace. We maneuvered and landed without incident. I immediately began looking for answers as to what happened. Inspection of plane showed no surface or control surface damage. We checked our controls and they were all free and clear. We powered back up and did Autopilot test and everything functioned normally. I spent the evening reviewing flight data and concluded that I failed to maintain a proper airspeed at the higher altitude to maintain my VS I entered. This is the first time I changed my approach to climbs from IAS to VS. I did something different from my normal process and didn't properly monitor my TAS as I climbed thru flight level 330. In the future I will never climb in VS. I think changing my flow from what I had been doing thru my entire flying left room for errors. I should have briefed my non flying pilot that I was doing something different so they had notice to back me up. I'm thankful for the job the ATC guys did to give us priority and be patient. Both of us as pilots stayed calm and flew the plane as taught but I'm embarrassed that my lack of monitoring airspeed in the late climb put us in this position.