I have a Lodge Logic cast iron pan that is seasoned very well. Lately I've been cooking grilled cheese sandwiches, which are supposed to come out great in a cast iron pan, but they're cooking very unevenly. Specifically, the edges of the bread (not just the crust) are almost burnt before the middle of the bread is even toasted. I've tried putting weight on the sandwich to press the whole thing down but that hasn't worked so I guess the heat is simply not reaching certain points on my pan.
I just read this NY Times article that seems to say this is often the case.
So, is there anything I can do about this? I've also tried heating the pan longer before cooking but that hasn't solved it. I want my sandwich to look like the perfect ones in the pictures!