Heat a large non-stick skillet on medium heat.
If the skillet is large enough to lay out 4 slices of bread, add half of the butter to the skillet. If the skillet is just large enough for 2 slices of bread at a time, use about a quarter of the butter (a little less than a tablespoon).
Let the butter melt. Watching it closely, stir the butter until it starts to turn a golden color.
As soon as it turns a golden color lay each piece of bread in the skillet. Move the slices around to absorb all of the butter in the pan.
Let cook until the bottom sides of the bread are toasted. Then transfer the toasted bread from the pan onto a plate for a moment.
Add the remaining butter if the skillet is large enough for 4 slices of bread. If cooking two at a time, add about another tablespoon of butter to the pan.
Stir the butter as it's melting until it turns a golden color.
Next, put the slices of bread back into the pan with the toasted sides up.
Add the cheese to each toasted side of the bread. Add the onion rings on top of the cheese (optional).
When the bottom sides of the bread are lightly browned, make a sandwich out of the slices of bread and cheese.
Cover the pan with a lid and turn the heat off while the cheese melts.
When the cheese is completely melted, cut in half and serve right away.