Got it: Leave the outter ring in place, insert an 8mm hex key through the outter ring and loosen the inner bolt; It will will push against the outter ring and release the crank.

Once the left-side crank is gone, use a rubber hammer to hit the right-side (drive-side) crank and slide it through the cartridge.

But even after cleaning and greasing the cranks, I could still hear the creaking noise on the drive-side.

So I went ahead, and loosened the two rings (cups?) to remove the cartridge bottom bracket. Applying some grease did the trick. I also noticed a plastic tube sitting in the middle of the bottom bracket, between the two rings.

Thankfully, I didn't break anything, as this was the first time for me and no one at the workshop was used to cartridge BBs.

I noticed that when tightening the drive-side ring, at some point, it becomes loose again: Maybe the left-side ring takes care of keeping the whole thing nice and tight.

I've been riding this bike every day or so for a couple of years, so might get a new BB now that I know how to get it installed.

Thanks much for the help.