Pan stain after roasting cheese
The most likely explanation is that your pan starts failing. When ceramic pans fail, they do so by getting gummed up with food buildup. 

I am a bit surprised to see it first occur with cheese, but maybe you dipped it in batter before frying? Also, the herbs on it could have been mixed with starch before being applied to the cheese, this is done to prevent caking and mold. Typically, the worst combination for these pans is starch with fat. On the other hand, I have no proof that it can't happen with cheese, it's just that I haven't heard of it being the first food to start sticking. 

Once this happens, you can't really clean it. A lye solution will restore it for a short time, but I don't know the physics of the pan failure, so I have no idea if it is beneficial, or on the contrary, if it speeds up the degradation process. 

Just continue using the pan, and once it becomes too non-nonstick, decide if you want to keep it that way and fry with it as with a standard pan (it behaves much like a stainless steel pan afterwards) or throw it out. For me, it depends on the pan heating quality, if it is a good pan with thick bottom and even heating, it continues doing a good job after the coating fails.