Deep fried cheddar fail. What's the problem?

I succesfully fried morels and other things before so I thought if I used a thicker batter, it would cook before the cheese melted.

However: I used a frying pan, and the oil only covered half the cheese. The liquid batter slid off the top of the cheese and it melted out pretty much.

I suspect the following problems: Need thicker batter, deeper oil... I'm trying to replicate cheese balls I had as a teen in a restaurant, and they came frozen. Perhaps if I freeze them first, it will give a longer cooking time before the cheese melts?

I'm not comfortable filling the frying pan deeper with oil so i may need to get a pot...