How to make Chad's perfect grilled cheese sandwiches:
. . . slow cooking is critical. The goal, after all, is to get a sandwich where the cheese is melted all the way through, while the bread is golden brown but not burnt. So, you put the burner on very low (just above the "simmer" region on our stove), melt a little butter in a frying pan (some people butter the bread, but if you're using good bread (and why wouldn't you be?), it's hard to do that without messing the bread up), mop up the melted butter with the bottom slice of bread, and cover the pan. When the bottom is sufficiently toasted (it takes a few minutes), take the sandwich out, melt some more butter, and repeat the process for the other side. If you do multiple rounds, it goes a little faster on the later ones, as the pan is already hot-- you may even need to lower the heat to keep from burning the bread.
Cover the pan, cut the sandwiches in half when they're done, and eat as hot as possible.