The panino con supplì is carb wrapped around carb, and the molten core is the entire reason it exists. A supplì is the Roman fried rice croquette: risotto bound with tomato and ragù, packed around a nugget of mozzarella, breaded and deep-fried until the shell is hard and the cheese inside has gone to a string that pulls into long threads when the thing is torn, the supplì al telefono. Putting that whole fried object into a roll is the sandwich. There is no thin filling and no spread; there is a crisp-shelled, rice-dense croquette with a liquid cheese centre, and the bread is there only to make a deep-fried snack something you can hold without burning your fingers.
The craft is timing and heat, because everything good about it is fleeting. The supplì has to go into the bread hot, straight from the fryer or close to it, since a cooled one has a tough shell and a set, rubbery core and the mozzarella no longer strings. The roll is plain and soft on purpose, a rosetta or a simple bun, doing no flavour work at all; its only job is to absorb a little of the frying oil and insulate the hand. The croquette is usually pressed lightly into the bread so the shell cracks and the centre starts to give, which is the point of eating it this way rather than out of hand. Nothing is added: the rice already carries the tomato and the ragù, the cheese is the payoff, and any sauce or leaf would only get in the way of a contrast that is already complete between crisp shell and stringing core.
The named variations stay Roman and stay close to the fryer. There is the classic ragù supplì in bread, the cacio e pepe version where the core is pecorino rather than mozzarella, and the build that adds a second fried thing, a crocchè, for an all-crust bite. Its Sicilian cousin the arancina and the rest of the fried-street repertoire follow their own logic and deserve their own articles rather than being crowded in here.