I think this is a fairly common homey dish in Japan. Essentially, this is a cheese stick (Japanese "processed" cheese) wrapped in Gyoza or Wonton skin and fried.
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.
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.
I served this with Dijon mustard. Either the smoked or non smoked cheddar cheeses were good. This type of snacks can't go wrong albeit it may not be too healthy.