If you have a second, identical working board, you can use an external programmer to "read" the chip and save it as a .bin to flash onto the broken board. How to Flash the BIOS Binary
Manipulating BIOS files carries significant risk. nutmeg-mini-itx rev 1.0 bios bin file
If the software fails to read the chip type, check the alignment of the SOIC8 clip pins. The tiny legs on older boards gather oxidation over time; gently clean them using a toothbrush and 99% isopropyl alcohol. If you have a second, identical working board,