Reinstalling macOS/OSX on new HDD - Mid-2011 iMac

The HDD in my Mid-2011 21.5-inch iMac failed a while back (ran AHT twice and this confirmed it). A third party technician took it in to recover the data due to me being unable to at the time. I got the machine back and tried to boot into recovery mode, only for it to cut straight to internet recovery, which resulted in a blank screen (I assume the machine never had the internet recovery firmware update). I had another relatively new hard drive with CloudReady installed on it gathering dust, so I installed that into the machine without formatting, as I assumed this could be done later. I fired up the machine again with the new HDD. Again no recovery mode (no surprises), and again internet recovery resulted in a white screen. So I held down option after a restart, and the new drive IS being recognised under the name EFI Boot, but a black screen went attempting to mount it.

I did some more research, and discovered that my iMac shipped with OSX 10.6.6, and thus I should have an install disk somewhere. Well, I couldn't find that. So currently I have no clear method of reinstalling OSX 10.6.6, any genuine help here?