Is anyone aware of specific problems with Vanmoof cranks/bottom brackets?
I've got the same problem on (what I believe is) a 2013 3.1. I was going to try replacing/upgrading the bottom bracket myself soon, hoping to smooth out the ride.

Unfortunately, I haven't been able to find the size online so I'll need to take it out and inspect before I can order a replacement, hopefully this goes smoothly.

Either way, I'll update with my results when I have them.

Update: Replaced with Suntour 68x118mm Square tapered BB from local (Arlington, MA) bike shop and removed chainguard (personal preference).  Awful sound is gone... For now.

Your mileage may vary. Good luck!