The Panini Thon is the pressed Italian-bread sandwich filled with tuna, and the tuna is what makes it the trickiest of the common paninis to get right. The bread is the soft, slightly sweet pain à panini, split, filled, then clamped onto a ridged hot plate until the outside is barred and dark and the inside has gone soft. Inside is tinned tuna, usually bound: with mayonnaise, or melted cheese, or both, frequently with tomato, occasionally with capers or sliced olive. It is the French panini that owes the most to the Italian tonno e mozzarella and the most to the lunch-counter tuna mix.
Tuna under a hot press is a moisture problem in the other direction from chicken. Tinned tuna already carries oil or water, and a mayonnaise binder adds more, so the danger is a wet filling steaming the soft crumb from the inside until the bread collapses. The working versions drain the tuna properly and use the binder to hold it in a paste that stays put rather than running, with cheese acting as a second seal between the fish and the bread. Get that balance and the press warms the filling through while the enriched bread takes its fast dark color outside and stays pliable within. Get it wrong and you have a hot, soggy parcel that falls apart in the sleeve. It comes off the plate very hot, goes leathery if it sits, and is eaten standing within a minute or two. Order-and-press counter food.
Variations argue about what joins the tuna. The tuna-and-mozzarella build is the most Italian; the tuna-mayonnaise-and-tomato build is the most French lunch-counter; capers, sliced olive, or a little red onion turn up where the counter wants more bite. The ham-and-cheese and chicken paninis are the other two staples and get their own entries. The Panini Thon belongs with the pressed and non-baguette breads the catalog groups under Pain Garni & Non-Baguette Breads, the shelf of French sandwiches not built on a baguette. Its particular contribution is the hardest version of the pressed-sandwich balance: a wet, tinned filling that has to be tamed before the heat can be trusted with it.