Hat tip to a commenter in this thread: http://www.techadvisor.co.uk/how-to/windows/how-find-windows-10-product-key-3632749/
From an elevated command prompt type:
wmic path SoftwareLicensingService get OA3xOriginalProductKey
That will read the key embedded in the BIOS. Windows 10 is supposed to be smart enough to retrieve it automatically but didn’t on two PCs I was clean installing.