Thank you for contacting the Intel Communities.
In this case my recommendation would be to check if you are using the latest graphics driver from our website.
If yes, please uninstall the driver from the device manager, restart the system and install the latest driver downloaded.
Also, here you can find the requirement to get 4K resolution out of the NUC.
1. Single DisplayPort 1.2 with 4K support.
2. Capable 4K display.
Supported resolutions and amount of displays:
Thanks for the reply. I had already done everything suggested and was using the latest driver. It turned out the problem was a bit odd.
I bought a new DP to HDMI adapter cable. I had been using a DP-to-HDMI cable but a different brand. Even though the windows generic driver would do 4k over the first cable, the intel driver would not. As soon as I plugged in the new cable and rebooted, new resolutions appeared for the Intel driver. (All the way up to 4096x2160 - too small for me!)
While your answer didn't prove to address the root cause, at least it confirmed I was going about things in the right way. A new cable...go figure.
I am glad to hear that you were able to get the resolutions desired.
Regarding the use of adapters, the recommendation is to use straight connections to make sure the signal is strong and will provide you will all its capacity.
Chances are the other cable was not strong enough to provide with the correct signal to the display.