Translation:The cook puts some butter in the frying pan.
Both English and Swedish tend to use på/on in cases where you put things on top of something which has a flat top surface, and i/in in cases where you put something into something that is more like a container. The frying pan is not seen as totally flat here, but more as a container. The butter can be liquid and still stay in the frying pan.
A typically flat thing is a cutting board (en skärbräda), if you'd put the butter there it would be on/på respectively.
See Arnauti's comment above. Using 'on the frying pan' isn't idiomatic in English I'm afraid. Although I definitely think it's fair to use 'on' instead of 'in' when adding ingredients as you go, but only if you don't follow with saying 'the (frying) pan.' For instance, 'I'm putting the peppers on,' or 'I'm going to put a little more salt on it' or something.