That's called String Cheese, and it's actually quite traditional to a number of cultures ... Italian, Armenian, Mexican, Slovak ... as well as Wisconsin. It's popular around the world because the technique for making it is easily learned and adaptable. You can even make it from store-bought cheese, as well as your own cheese.
- Make or buy a stretchy high-temperature (thermophilic) cheese, such as mozzarella.
- Heat the cheese in very hot water (traditional method) or the microwave (modern method) until soft, pliable, and stretchy.
- Pull the cheese out into a long strand, then double it over. Wear gloves, the cheese will be hot.
- Repeat steps 2-3 as many times as necessary.
- As the strands start getting thin, twist the cheese into a braid.
This is the sort of thing it's better to see than to describe, but I haven't been able to find a good video showing you how.