Get a pan on low-medium heat, placing about a tablespoon of butter in it. Once butter melts and begins browning, milk solids will create a film over top of the butter, remove with a spoon until most of the milk solids have been removed.
While you are waiting for the butter to clarify, begin preparing your sandwich.
Break the lobster tail in half, removing meat and roughly chopping.
Spread mayonnaise on top and bottom slice.
Shred cheese, add 1/4 cup gruyere, then an 1/8 cup of gouda.
Chop up lobster tail, place on sandwich, adding some salt and pepper.
Top with 1/4 cup of aged cheddar cheese, and top slice of bread.
Brush both outer sides of sandwich with clarified butter.
In a pan on medium heat, fry until golden brown on each side, and cheese has melted.