Henry was a holographic waiter in the Bashir 62 holoprogram.
During the jack-in-the-box scenario, Henry served Tony Cicci a cheesesteak sandwich that Cicci was less than impressed with. Cicci proceeded to display his dissatisfaction with the sandwich to Henry before cramming the uneaten portion into Henry's face while throwing him to the floor and demanding that he get him a new sandwich, even if he had to go all the way to Philadelphia to get it. (DS9: "Badda-Bing, Badda-Bang")
Henry, whose name was not spoken on screen but came from his name tag, was played by stunt actor George Colucci, who received no credit for his appearance.