Which converter do you have? It must be an active one. I use the Club 3D mini-DP to HDMI 2.0 one with good results (on Arch). You have to use reduced blanking timings as (for whatever reason) the NUC can only use a pixel clock of about 540 MHz.
For example this works for me:
xrandr --newmode "3840x2160_59.95" 533.6 3840 3982 4027 4064 2160 2170 2180 2190 +hsync +vsync
xrandr --addmode DP1 "3840x2160_59.95"
xrandr --output DP1 --mode "3840x2160_59.95"
I used 59.95Hz timings as that is 2.5 times the usual film frame rate.
On my TV I had to disable Deep Color (HDR signaling) on the HDMI port. I'm not sure why, as the HDMI converter is said to be able to do color space conversions (e.g. from 4:4:4 to 4:2:0). Maybe the DP bandwidth is too high for the NUC's cdclk limit.
Also there is some code in the i915 driver which adjust cdlk for Broadwell but currently uses a limit of 540MHz, even though with adequate cooling (which I'm sure the NUC has) a limit of 675MHz is allowed. It's just that the code doesn't know whether the cooling solution has enough headroom. You could easily patch that part and have a higher cdclk limit. (see function intel_update_max_cdclk() in intel_display.c)
This message was posted on behalf of Intel Corporation
Please bear in mind that Intel limits the support for Linux operating system.
I would recommend checking for Linux drivers at: https://01.org/linuxgraphics/downloads/2013/intelr-graphics-installer-1.0.1-linux
Some customers have reported that ArchLinux* has been working properly on your Intel® NUC