TLDR; Close the "Manage Bluetooth Devices" screen.
I must have been good this year because Santa put a pair of the Bose QC35 wireless, noise cancelling headphones under my tree for Christmas! While the headphones are truly excellent, especially the noise cancelling, they're not the subject of this post.
Rather, it's a nasty little bug I ran into when trying to connect them to my Macbook Pro running Windows 10 under Bootcamp. I didn't have any trouble pairing but as soon as I started the music, all that came through was a stuttered mess of noise...
Queue the next 5 hours spent digging through the depths of Google, trying different suggestions and ultimately ending up with nothing to show for it except that the Windows drivers Apple supply for the Broadcom Bluetooth chipset are somehow substandard - especially when it comes to Bluetooth audio. Seemingly a dead end...
I was thus a surprise when I turned on my laptop this afternoon to have one last tinker and clear, crisp audio started playing! WTF?! Seemingly nothing had changed!
After a bit of back and forward, trying to disconnect and reconnect the headphones I managed to replicate the issue. And it all boils down to this: if the screen to manage Bluetooth devices is open, you will have stuttering sound. Close it and boom, it's fixed!
I would assume that the issue exists because the driver isn't able to search for new devices and play audio at the same time. That being said, it's a particularly irritating bug as this screen is more than likely to be open after connecting your headphones and testing that they work correctly!
A couple of people have commented on this post and I thought it would be worthwhile summarising the salient points:
Closing the Bluetooth window mostly solves the issue but you may still experience a "blip" every now and again. This may be the presence of other QC35s in my office or maybe just other Bluetooth devices? In any case, I've now resorted to hard-wiring them when sitting at my desk as the blips can really throw off my concentration.
Joris reported below that he's getting the same issue on his windows PC that isn't running under Bootcamp! So the issue is more widespread than first thought. Poor show Microsoft!