The half-smoke is defined by the sausage itself, which is the rare case in the hot dog family where the meat, not the build, is the argument. It is a coarse-ground link, roughly half pork and half beef, smoked and seasoned with more spice and a heavier hand than a standard frankfurter. The grind is the point: where a hot dog is emulsified to a uniform paste, the half-smoke is left coarse enough to have a visible, chewy texture and a real bite. It is also bigger around than a frankfurter, which forces every other decision in the sandwich.
The craft follows from that thicker, smokier link. The half-smoke is usually split lengthwise and griddled or grilled so the cut faces caramelize and the smoke comes forward, which a boiled hot dog never does. Because the sausage carries so much weight and grease, the bun has to be sturdier than a standard steamed roll or it collapses under the load. The standard dress is chili, chopped raw onion, and yellow mustard, and the chili here is doing structural work as much as flavor work: it binds the split sausage to the bun and adds the moisture the griddled link has lost. The onion supplies the cold crunch and the sharp top note that cuts the rendered fat; the mustard supplies the acid. Built this way it holds together long enough to eat standing at a counter, which is how it is meant to be eaten, fast and over a tray.
The variations stay close to the District. The plain half-smoke, split and griddled with nothing but mustard, is its own honest thing. The chili half-smoke is the canonical loaded build. Cheese, slaw, and a heavier chili push it toward a fuller plate. It sits in the same family as the Chicago dog and the Coney Island hot dog, an idea adjusted for a local sausage rather than a local sauce, and those relatives deserve their own articles rather than being crowded in here.