What's your favorite local specialty food in Japan?

It's a bit under the radar, but I recommend yakimanju, a local specialty from my home prefecture of Gunma! It's a regional dish where fluffy, bread-like buns are skewered and grilled until fragrant, then slathered with plenty of sweet-and-savory miso glaze. Despite the name "manjū," there's no red bean filling.
In Gunma you'll find shops that serve it, and it's also a festival-stall classic. The balance of sweetness and saltiness is perfect—and totally addictive!