Place one slice of cheese on top of each toasted side bread slice.
Mound tuna salad on top of cheese, spreading it in an even layer, then top each with remaining slice of cheese.
Top with bread slice, toasted side down. Add an additional nob of butter to pan and return your sandwiches. Press with burger press and cook for about 3-minutes, being careful not to burn.
Flip tuna melt, cloche (a stock pot lid will do) with a spritz of water and cook until second side is well toasted and cheese is melted.
Slice in half and serve with a pickle.