B737-800 Captain reported the thrust levers auto advanced re-accelerating the aircraft after touchdown requiring immediate action to move the levers to idle and slow the aircraft down.

Narrative

I was Flying Pilot (FP). Of note auto brakes were MELed INOP and Runway XX was dry. I briefed an approach to ILS XX at ZZZ. As it is a relatively short runway (7;001 ft.) and we had INOP auto brakes I briefed that I would touchdown at 1;200 ft. on the runway and use max manual braking and max reverse thrust and turnoff at XX Taxiway. During the landing flare I reduced thrust to idle and touched down with the thrust at idle. I would also like to note this was not a bounced landing. Speed brakes deployed normally. After touchdown when I was reaching forward from the thrust levers to deploy the thrust reversers I felt the throttles start to advance. At that time the speed brakes also stowed themselves as the thrust started to increase as the thrust levers re-advanced themselves. I felt the aircraft start to reaccelerate so I quickly closed the thrust levers to idle which they then stayed at. I also started applying max manual braking. Fortunately the First Officer (FO)/Monitoring Pilot (MP) noticed the speed brakes retracting and re-extended them for me as I dealt with stopping the aircraft. Because of the startle factor associated with these various events occurring I forgot to use reverse thrust. Fortunately this did not affect our stopping distance as Runway XX was dry. In any case I was still able to turn off at the pre-briefed XX Taxiway.The unexplained advance of the thrust levers after touchdown [caused this event]. As I stated I brought the thrust levers to idle in the flare and touched down with the thrust levers at idle. The aircraft touched down and settled normally to the runway and there was no bounce landing involved. I am still at a loss to explain why this happened. Fortunately I had briefed for a landing on a short runway and used the tools I had except for forgetting to use reverse thrust due to the startle factor. This did not affect landing distance but if this had occurred on a contaminated runway forgetting to deploy the thrust reversers could have led to a runway overrun which would be disastrous on Runway XX at ZZZ.Hopefully Boeing or my airline could brief us why this would occur during a normal landing touchdown. As I previously stated I have no idea why this occurred. I do know this same problem has been reported at my airline by other pilots of this type of aircraft.