My 2013 R56 S has been making this very loud valvetrain-esque noise when the engine isn't up to temp yet and only when using light throttle, like when leaving my neighborhood.

To describe the sound, it's like a loud knocking that gradually comes in over a second or two. If I give the car more gas, it goes away. If I let off the throttle, it goes away. It never happens when the car is warmed up, and it never throws a code.

I attached a sound clip, which isn't the best example as it's a bit hard to hear the difference. In person it's quite pronounced. The noise comes in around the 5 second mark and stops when I let off the gas at around 10 seconds. To me, it seems possibly VANOS related? I already had to replace my intake vanos solenoid due to a CEL but did not replace the exhaust side. The intake vanos solenoid was sparkling clean when I replaced it, so I figured it wasn't due to residue build-up and didn't think to replace the exhaust side, too.

Yes, the car has always been topped up with oil Just thought I'd mention that... And it runs great otherwise.

Has anyone else had this happen? Any ideas?