I was going to suggest a screw extractor. However, it may be necessary for you to find a machinist who has a small mill. In that case he can try to run a small mill in slowly to clean up what's left and then try to retap the hole. Usually when you do that, the tap will grab what is left and you can unscrew the tap and bring the broken part out, just as a screw extractor would. From the picture it appears you are talking about the tripod mount on the scope itself, rather than on a tripod. That may be a more ticklish matter and might require a trip back to Swarovski. If that is on the scope itself, a broken screw extractor is not going to work because it needs to go in further than the scope body will allow in order to work. A bottoming Tap as opposed to a regular tap might be your only alternative short of the factory. If that's what you want to try, see if you can find a machinist to at least clean up the hole for you. Then measure the size and check a tap chart for the closest you can get to the hole size and use a bottoming tap, but do it slowly and use tap lube on the tap. If you are not sure how to tap a hole, find someone among your circle of friends who is and ask them to help. Failing that, see if you know an auto mechanic who has a machine shop with possibly a milling machine. He could help you with a tap. Turn it in a few threads and as it gets tight back it up a thread or two and then keep going. Eventually, the remains of the screw that snapped off should back out with the tap.
The picture looks bad and don't kid yourself, it could very well be. Don't try using heat on it, although a little warmth might help but not heat. Try finding something that is liquid that you could put in the hole to help seep into the threads to help them separate from the scope body. But don't overdo it.
Good luck.
!!! Probably should have sent it back in the first place!!
