Having spent my formative years in Wisconsin, I can't help but love cheese. So, when it comes to a good old-fashioned grilled cheese sandwich, I like it golden on the outside and gooey on the inside. Who's with me on this? So next time you want a perfect grilled cheese sandwich but just can't get the cheese to melt before the bread burns, remember this little trick: put a lid on it!
Set your stove on medium low (on mine it's at 3.5 out of 9)
Cover the sandwich with a lid.
Cook the first side for 5-6 minutes as the pan heats up, and then the second side or any subsequent sandwiches should take 3-4 minutes to toast perfectly.
Unfortunately, some slight adjustments may be necessary depending on your stove, pan, and how much cheese you put on, but the principle remains: put a lid on it! And don't worry, the outside will still get crispy as long as you don't turn the heat off and leave the pan on to keep it warm for an extended period of time.
As a bonus fact: I always thought the butter was what made it crispy. I was mistaken. Butter is not mandatory (although it is yummy). I figure I'm already getting more than enough fat on the inside of the bread and don't need to be spreading more on the outside, but the choice is yours.