Butter one side of each slice of bread and set aside.
Add 1 tbsp of olive oil to a non-stick pan and add the julienned onion. Cook for about 3 minutes, and then add salt and pepper. Cook for an additional 4 to 5 minutes, until they start to brown.
Add 1 tbsp of soy sauce and continue cooking for about 2 minutes, until they get really dark.
Shape the onions into a rough rectangle using a silicone spatula. Add a slice of cheese, together with the shredded cheese on top of the onions. Allow this to cook for one minute, until the cheese starts to melt.
Add the bread over the top of the cheese, NON-buttered side down (so that the buttered sides are facing you). Flip the entire thing, so that both pieces of bread are now on the pan.
Flip one piece of bread over the top so that you have a sandwich. Cook for about 2 minutes and then flip. Cook for an additional 2 minutes.