I just had one of these, and I realized that I've never shared this little trick with you guys.
It's weird, but it works. And, I first read about it on eGullet, so I'm not the only one to do this.
Don't put any butter or oil in your pan. Don't butter the bread. Instead, spread the outside of each slice of bread with a VERY thin layer of...
I'm totally serious. And, no, it's not gross at all. Think about it. Isn't the crust on French Toast wonderful? It's made by eggs that are fried in oil or butter, right? You dip the bread in egg and then fry it in grease. Mayo is comprised of egg and oil, so the French Toast effect is what you can achieve by using mayo on your grilled cheese.
If you don't believe me, try it for yourself, and while you are at it, add half of an avocado, sliced, and a small drizzle of raspberry vinaigrette.