Muffin. It tastes excellent in a McDonald's Egg McMuffin with cheese, therefore it should taste well in a grilled cheese sandwich.
You can find many recipes online, not that you need one, but you may be inspired to make your own.
Rachael Ray shared inside-out English muffin grilled cheese sandwiches in 2010. White muffins work just as well as whole wheat or whole grain English muffins
Food Network provided another version of the dish (also by Ray) in which the muffins aren't flipped inside out.
Food & Wine states that an English muffin's nooks and grooves are great for melting cheese.
Plus, the muffins' compact size lets you make mini sandwiches without cutting them in half