What? and risk nightmares?
Actually two ways:
Most people butter one side of two slices of bread. They assemble it as sandwich, with the buttered side out,cheese in the middle and cook in fry/frying/saute pan (or on a flat griddle, or in a sandwich maker) and "toast" flipping it over to cook both sides. It is called amazingly enough--grilled cheese (sandwich) It can be fancied up with bacon, or tomatoes. It is most commonly made with the "plastic" processed American cheese.
For an open face (one slice of bread) sandwich, we'd use a toaster oven. but then it would be a melt-- as in a Tuna melt-- bread with tuna salad, (tuna, chopped veggies and mayo) a slice of tomato, and cheese on top.
There are other melts, but I think tuna is the most common.
A toaster oven would toast the underside of the sandwich (bread) and at the same time melt the cheese.
A toaster oven is about the size of bread box, and it's close to being the #1 appliance in states. i'll look for a site with an picture since Jo didn't have a clue what a toaster oven was. Either it's very american or goes by an other name elsewhere. (and welsh rabbit -- what do they call melted cheese sandwiches in Wales?)
An american cheese sandwiches are really goo-ey cheese encased in two slice of bread. They are not really melted cheese (a la fondue) poured over toast (points) which is how welsh rabbit is portrayed in american cookbooks.
OP
