I should have mentioned that I've already searched HP's website. HP's Drivers and Software download page for this PC does not have a BIOS update. Other HP PC's do have BIOS updates on their equivalent page.
If there is not an update available from HP, You could try the Foxconn website, but I doubt that you could find what you need there. Generally, the vendor is the only source for updates to the BIOS. Even if the motherboard is made by some 3rd party, there is enough "customization" applied to the board, that the 3rd party doesn't supply the BIOS, and if they did, it might not support some of the HP specific features of the motherboard.