How do they wind self-supporting coils like this?

It is wound on a form, Glued with quick setting cement and slid off.

Your question lacks certain background information needed to give you a real answer. The first question I have is production quantity. The greater the quantity the more automated it needs to be. So I can't answer your question unless I know the level of automation vs human intervention. The next question has to do with tolerances. How much slop is acceptable? If you require perfection and consistency, that dictates how the production machine needs to be made. The next factor is based on the cost of human labor. Are you paying $1 a day? If you are, that changes the economics compared to $20 an hour. The next factor is how long do you wish to make this part? If this part requires a ten year production run, that changes what kind of investment is appropriate compared to a production run of a month. Once you provide these details, there are certain to be more that arise in the conversation. By the way, if you chose to outsource the design of production equipment, they will ask the exact same questions.

I am sorry if it sounds like I am evading the central question, but without these details, it is not possible to provide meaningful suggestions how to make this part.