First off, I'm not sure if this is a grilled cheese or a melt or toast of some kind.
What I normally do is that I take 2 slices of bread, 2 slices of cheese, put the cheese between the bread and then stick it into a panini press until slightly golden (that's how I like the bread).
Sometimes the cheese makes its way out from between the bread slices and oozes on the griddle and then gets fried. I love it when that happens, because that fried bit of cheese at the edges of the sandwich is my favourite part. It gets a crispy texture where it touches the griddle, becomes golden brown, its still sorta gooey and stringy on the inside. Most importantly, it really opens up the flavour of my cheese. It somehow has more flavour than the majority of the cheese that stays between the bread slices and just melts.
So then I had my genius idea. I'll make the same sandwich, except I'll put the bread slices side by side and top them with one slice of cheese for each. Basically I put 2 open faced cheese sandwiches in the panini press and when they are good and ready, I'll just put the two faces together so that I can have one sandwich with 100% of the cheese touched by the griddle and becometh golden-crispy-stringy-gooey perfect with amazing flavour.
At first I suspected that the exposed cheese might become stuck to the panini press, rather than the bread, and that I may end up in a gooey mess. However, the non-stick cooking surface released the cheese side without issues and I was able to get both sides out and assembled just as I had planned.
Despite this initial success, the sandwich was a complete disaster. For one, I had to cook the bread side to a much deeper golden brown than I'd like, to get any colour on the cheese. The bread was crispy throughout and not just on the surface as I like. What's worse, I couldn't taste the cheese at all! The flavour was all gone, vanished! Like I didn't think possible. Same amount of cheese, no flavour, it just tasted slightly greasy. The cheese also failed to attain that thin crispy golden crust. Instead, it had remained mostly yellow and had only hardened somewhat into something rather dense and leathery.
How could this have failed so badly? I couldn't believe it, so I tried again with a different cheese. Instead of the 1.5 month gouda that I normally use for this, I used a 3 month tilsit that was the most intense meltable cheese that I had at hand.
Once more, the sandwich turned out hard and flavourless. I had to make another sandwich the regular way to cope with these two consecutive failures. Why did this not work? How can I make it so that all the cheese is like the cheese that drips out from the sides? My truest thanks to anyone who answers.