First, I downloaded firmware upgrade (for Windows, sp91622.exe) from HP support site and extracted files from downloaded
I then extracted correct CAB for my laptop. You will need to find out what chip your laptop uses. It can be read from firmware system info. CAB with matching filename is the right one.
$ 7z x sp91622/68ICF.CAB
I was initially overly positive and thought I could just copy everything to USB-stick and upgrading would just work from current firmware. Well, things don't work like that in HP land. After some trial and error I found out that files need to be in particular paths, with particular filenames which of course are nothing like they are in the archive because reasons.
$ mkdir -p EFI/HP/BIOS/New
$ mv efibios.sig Rom.* ver.* EFI/HP/BIOS/New/
$ cp -R sp91622/BIOSUpdate EFI/HP/
$ cd EFI/HP/BIOS/New/
$ cp Rom.bin 68ICF.bin
$ cp efibios.sig 68ICF.sig
$ cp Rom.sig 68ICF.s12
After all that nonsense, I copied EFI directory to USB-stick, rebooted the laptop in question and entered boot menu with F9. From there I ran EFI/HP/BIOSUpdate/HpBiosUpdate.efi and the upgrade finally worked. I suppose these upgrade files could also be copied to system EFI-partition and run from there, but I didn't have one so, USB-stick it was.