You install Windows normally, choosing the internal drive (or even another external drive if you want a portable Windows). The external installation drive stays untouched unless you deliberately format it.
You plug the external hard drive into a working computer. It’s 500 GB, mostly empty. You know Windows setup won’t need all that space, but the drive has to be bootable. install windows from external hard drive
Then you use bootsect /nt60 F: (where F: is your external drive) to write the Windows boot code onto it. You install Windows normally, choosing the internal drive