Apparently this issue has to do with adaptability in throttle control.

I had done the throttle adaption reset method and it went away for a while but then it came back, again only periodically. definitely has something to do with a standing start acceleration .

Here one link that describes what I’m talking about

https://xoutpost.com/bmw-sav-forums/...esitation.html

There are more on various forums. Google “throttle delay e53” and you will see what I mean.

For example:
https://xoutpost.com/bmw-sav-forums/...tle-delay.html

Car has no codes no other drivability or running issues.