I'm having a similar issue with static and black screen on this NUC. However, it's intermittent. It normally happens after waking the NUC up and then trying to watch a video. The video will start playing for several seconds and then static. The sound keeps going, like the video is still playing, just the video is static. I have to power off the NUC and back on - then I'm good for awhile. I'm connecting to an LG OLED65E6P through an Onkyo 4K receiver.
I'm going to try swapping HDMI cables tonight - but it's weird that it'll work fine for hours, and even days sometimes. Then it static's out and does it a few times.
If it helps, I've got the latest drivers installed - running 4K resolution (60p), with all video options disabled or set to driver defaults. Display is set to YCrCb disabled (some suggested with a 4K TV, that should be enabled - but when I do, I get the screen in yellow).
I'm hoping it's just a driver issue that will be resolved soon with the next release.