I have 4 different computers with Windows 10 (2 with Pro and 2 with Home) 64 bit. 2 of the computers are desktops that I built and installed Windows 10 Pro on. The other 2 are laptops on which Windows 10 Home came already installed.
I have made recovery drives for all 4 computers and have done them with the system files included and also without. Regardless of how I make them, none of them have the option to "Reset This PC" as shown in the screen shot in this tutorial.
On the main screen of all of the recovery drives I have made, it has a "Recover from a drive" and "Troubleshoot" options. On the "Troubleshoot" option, it says "Reset Your PC or see advanced options." When I click on "Troubleshoot," it gives me 6 options, but none of them are "Reset This PC." All 4 computers have a recovery partition and an EFI system partition.
The main reason I need this option is because I work on other people's computers occasionally and rarely do any of them have the entire computer or their user created files backed up, nor have they created any kind of rescue media. I recently worked on a friend's laptop that had got so corrupted, it wouldn't boot. Every attempt to restore it, such as system restore run from a recovery disk and drive, and running the reset and refresh this PC options (systemreset and systemreset - cleanpc) from an administrative command prompt, resulted in error messages.
I told him I might have to wipe the drive and reinstall Windows and he was adamantly opposed to that. I borrowed a recovery drive from another friend that had the "Reset This PC" option on it, and was able to restore my friend's laptop without him losing his files. I asked the other friend how he created the recovery drive to get the "Reset This PC" option on it. He said he didn't do anything special. He used the "Create a Recovery Drive" option from within Windows 10 Pro on a desktop PC he had built, and included the system files during the drive's creation.
So, is there some trick to making a recovery drive that includes the "Reset This PC" option that I am not aware of?

No. The laptop would not boot to Windows, advanced startup options, or safe mode. I had to used the Reset This PC option from a Windows 10 recovery drive that I borrowed from a friend. None of the 4 recovery drives I had made, nor an installation disk, had the Reset This PC option.

Any Windows iso can be used for Windows RE.
For example Windows 7 , 8 and 10 can be used.
The Windows RE on an iso comes with startup repair, system restore, command prompt, etc.
None of the iso come with a Windows RE option for reset.

On computers in which you can boot to the computer's windows RE there are often options for reset.
Unfortunately this option can be unavailable or malfunction when needed.

An alternative to reset save files that usually works is custom install.

At times it can fail too.

The Windows.old is restored and the result is similar to reset save files.
The partition structure remains the same as compared to clean install.

Custom Install Windows 10

Brink:
The build number on my friend's laptop is: 18363.836 - Windows 10 Home 64 bit. The build numbers of the PCs I used to make recovery drives are: 18363.836 - Windows 10 Pro 64 bit; 18362.900 and 18363.900 - Windows 10 Home 64 bit. One of the desktops that I used to make a recovery drive was just shut down less than an hour ago and I'm not restarting it just to get the build number.The language and all other settings (keyboard, region, etc) are the same on all of the computers.
Perhaps I'm missing the reason you asked for the build numbers and what you're going to try. The Reset This PC option does not appear even when I boot the computers with the recovery drives on which each one was created. Like I said in my original post, I made recovery drives for each of my computers (first) with the system files included and (then) without them. Whether the recovery drive had the system files on them or not, the Reset This PC option never appeared on any of the computers I booted to with the recovery drives, even though on the Troubleshoot option, it says "Reset this PC or see advanced options." The only recovery drive that I saw the Reset This PC option on was the one I borrowed from another friend, and it was made on a desktop PC with Windows Pro 64 bit. I don't know the build number of that system. But, even though it was made on a PC with Pro 64, it had the Reset This PC option and I was able to restore my friend's laptop with it, which has Home 64 bit on it.
Zbook - I had forgotten about the custom install option and the Windows.old folder. I don't work on/repair anywhere near the number of computers that I used to, or as frequently. That plus getting older and not remembering things as well as I used to...........Now, I do it only when a friend or relative has a problem with theirs.

Brink, Thanks for all of your help and advice on this. Good to know I didn't do something wrong if you got the same results as I did. Just had me wondering how one of my friends was able to make a recovery drive that had the Reset This PC option on it.