Go into the Contents/SharedSupport folder and open InstallESD.dmg; Now find BaseSystem.dmg and mount (open) it. The file is a 'hidden file' and will be slightly greyed out. Now you need at least 1.1GB of free space on a flash drive or DVD.

An interesting dilemma, indeed. The configuration of the Recovery HD seems convoluted and backward; why they'd put the entire startup system inside another disk image is beyond me--unless installing extra utilities is exactly what they're trying to prevent. I see two possible solutions:

1. After backing up BaseSystem.dmg, try using Disk Utility to convert the image to a read/write format. Make your mods, and convert it back. This option, of course, is highly tricky, and it’d be difficult to keep the volume bootable.

2. Use Disk Utility to create a new (standard, visible) partition in HFS+, and Restore from BaseSystem.dmg to it. You’ll now effectively have two recovery partitions. This new one, though, not being wrapped up in an image, should be free to add files to. It seems like Mac OS X Base System has all the requisite files for starting up from, all the way down to boot.efi. You might have to also jump through a few hoops in order to get it bootable, but it should be far more straightforward than using option 1. Once you’ve done that and tested it thoroughly, you could remove the “official” Recovery HD partition.

Might I stress: I have tried neither of these, and I’m running purely on speculation based on past experience. Proceed entirely at your own risk, and only if you know exactly what you're doing!

Here's a short guide on opening DMG files on Windows and extracting data from them.

1. Download DMG Extractor (it's free).

   Once installed, DMG Extractor will run automatically.

2. Open DMG Extractor and select the DMG file you want to extract

   Click the 'Open' menu icon on the top-left of the window.

   If the DMG archive is password protected, DMG Extractor will prompt you for its password:

3. DMG Extractor will load the file you selected. If you have a large DMG file, a progress bar will show until the DMG file is loaded.

   Now you should be able to see all the files contained within the DMG file and navigate folders and files.

4. Extract the files you want

   Click 'Extract', next to the 'Open' button. You can choose whether to extract the whole of the DMG's contents into the same folder, or into a specific one chosen by you. If you don't need to extract all the files, just select the files you want and on the 'Extract' menu click 'Selected files to…'

Can't Open Basesystem.dmg Download

That's it: extraction complete! Your selected files should now have been converted from the DMG file and saved onto your Windows computer ready for you to use.