The panino imbottito is the same idea as a filled roll said in a different, fuller register. Imbottire means to pad or to stuff, the verb used for upholstery and for a quilt, and it carries a sense the neutral farcito does not: the bread is packed, worked full, made to bulge. The term lives mostly in the South and in older usage, where a sandwich is expected to be a substantial thing rather than a light bar punctuation, and where the word itself promises that the roll has been worked full. It names a register more than a recipe, but the register matters: an imbottito is the generous reading of the Italian sandwich.
The craft is in being full without becoming a stack. Even at its most padded the imbottito tends to lead with one thing, a strong cured meat or a cooked vegetable that has been developed, and to build around it rather than layering many voices, so the fullness comes from quantity and from a sturdy bread rather than from a tower of fillings. The bread is chosen with structure, a crusted roll or a country loaf, because a packed sandwich left in a soft white bun will slump and go to grease before the last bite. A wet element, a marinated vegetable or an oily salume, is drained or balanced so it seasons the crumb without flooding it. The point is a sandwich that satisfies as a meal, which is what the word itself implies.
Its variations are regional and many, because every southern town has its own loaf and its own larder to pack into it. The neutral panino farcito is the same act named more plainly. The place-named rolls of Basilicata, the Marche, and the South each stuff a regional shelf into a regional bread. The street builds of Palermo and Naples are the imbottito taken to the fryer and the offal pot. Each of those is a distinct preparation with its own balance to strike, and each deserves its own article rather than being crowded in here.