Best I can tell it is going to be one of these three drivers. How do I learn which driver Debian Linux requires?
1) igb-x.x.x.tar.gz driver: Supports all 82575/6, 82580, I350, I354, and I210/I211 based gigabit network connections.
2) e1000e-x.x.x.x.tar.gz driver: Supports the Intel® PRO/1000 PCI-E (82563/6/7, 82571/2/3/4/7/8, or 82583) I217/I218/I219 based gigabit network adapters.
3) e1000-x.x.x.tar.gz driver: Supports Intel® PRO/1000 PCI and PCI-X family of gigabit network connections.
Only windows 10 is supported on your nuc.
Your nuc uses a Gigabit (10/100/1000 Mbps) LAN subsystem using the Intel® I219VGigabit Ethernet Controller
The windows 10 driver is here: https://downloadcenter.intel.com/download/28613?product=126147
You should contact the linux community for help.