The longest-running Hue specialty restaurant I can think of is the one on Senter Rd. They have been there for ages and (as far as I knew) used to be the only ones in town that served banh beo in the little individual dishes they were cooked in.
Since then, many other restaurants have joined in the game. Bun Bo Hue An Nam which has grown and opened up a second location. Hue Restaurant is a relative new-comer (2007 I think).
I haven’t eaten at any of them in over a decade so I can’t vouch for their quality. My favorite of all the little imperial treats that came from Hue is Banh Ram It. A steamed mochi dumpling filled with minced pork and shrimp and then put on top of another crispy fried piece of mochi dough. Crunchy, chewy, yummy! The ratio of steamed dumpling to fried dumpling has to be right though otherwise it can be too chewy, too oily, etc.
