Heat the vegetable oil in a frypan over medium heat. Add the onions and celery and season with a little salt. Cook and stir until tender, about 5 minutes.
In a medium bowl, stir together the tuna, mustard, mayonnaise and the sauteed onion and celery. Season with cayenne, seasoning, parsley and Tabasco sauce. Spoon onto half of the bread slices. Top each one with a slice of cheese and then the remaining slices of bread.
Spread butter onto the outsides of the sandwich. Fry in a frypan over medium heat until golden brown on the outside and cheese has melted, about 5 minutes total.