If you want to, take some screenshots around the incident, just before, during, just after. Make sure we can see the modes engaged on the autopilot, then engine instruments, the primary flight instruments.
Normally the autothrust will control the engines during a climb, with nominal power being climb thrust. This is signified by the "N1" showing on the mode annunciator in the electronic attitude indicator. The pitch of the aircraft is normally controlled by the autopilot to maintain a set airspeed (FL CHG mode) and should show "MCP SPD".
It sounds like you are climbing in vertical speed mode with the thrust controlling the airspeed, which is only recommended for short (step) climbs. However there are still some protection modes active that should kick in to save the aircraft in case of gross pilot error, so I am not sure how you get it to stall...
Another possibility is windshear or icing, try to fly with the weather set to no clouds and no winds and see if that changes anything.
Cheers, Jan