Stephen,
Your pic has not been released yet..... I'll assume it refers to the 03.07 latest version which is the latest for all 8300s (your SFF version is included).
There is a difference between the BIOS flash method and the DOS flash method. My bias is that the BIOS flash method is the safest of all possible methods because the OS used then is the most primative (BIOS is an OS, loaded from firmware). The DOS method uses a higher level of OS. The W7 method is a higher level yet again, and W10Pro64 is even higher. Go primative.
Added info:
DESCRIPTION: This package provides the HP Business Desktop System BIOS Package for 8300 models with a K01 BIOS.
EFFECTIVE DATE: June 20, 2018
SOFTPAQ FILE NAME: SP88543.exe (contains BIOS version 03.07)
SOURCE: https://ftp.hp.com/pub/softpaq/sp88501-89000/sp88543.exe
ENHANCEMENTS: Provides latest Intel Microcode versions 0x20 for Ivy Bridge processors and 0x2E for Sandy Bridge processors.
HP doc on the latest BIOS for the mitigate CVE-2018-3639 and CVE-2018-3640 issue:
https://support.hp.com/us-en/document/c06001626 and in this doc is the link to get 03.07, same as above.
Nice Intel PDF from this month you can search in easily to find your particular processor:
https://www.intel.com/content/dam/www/public/us/en/documents/sa00115-microcode-update-guidance.pdf