When I was growing up this was what my mother used to make as a drinking snack when guests came over. She deep fried this but I just fried all the surfaces using a small amount of oil in a non-stick frying pan (with the hope that this was slightly less deadly than my mother’s method).
Here I used smoked cheddar cheese cut into a stick that would just fit the Wonton skin. I wrapped it and sealed the end by moistening it.
Using a scant amount of oil (less than 1 tbs), I fried all four sides in a non-stick frying pan on low heat until all sides are golden and crispy. Depending on the cheese, it may melt or as in the case of smoked cheddar, it may soften but not actually melt much.
The image on the left shows cheese sticks wrapped with wonton skin before being fried. On the right is the finished stick made with aged but not smoked cheddar cheese which melted and puddled in the bottom of the wonton skin. If you use melting cheese, the cheese may leak from the seams of the wonton skin if you are not careful.