Somebody documented doing so over in How to prepare for reflashing firmware
I have reflashed the 11th Gen and Core Ultra 1 boards by hand. The important parts to know are that the flash parts are 3.3V on the older generations and 1.8V on the newer ones and that with the common CH341A-based SPI flashers you will need to hold the pogo pin jig in place for 8-12 minutes for a full read/compare/write cycle.
I have an encapsulated full flash image extracted from the 12th gen update (3.05?) around somewhere if you need it.
Given that you are seeing POST codes, that suggests the embedded controller is running just fine.