The Kansas City Reuben dog is a deli sandwich rebuilt on a frankfurter, and the swap of cured beef for sausage is the whole idea. It takes the four fixed components of a Reuben, sauerkraut, Swiss, Russian or Thousand Island dressing, and the rye logic, and runs them over a hot dog in a split bun instead of corned beef between two slices of rye. The dog stands in for the meat. Everything that makes a Reuben a Reuben is kept except the protein, which is the same impulse that turns any settled sandwich into a named regional variant: hold the system, change one part.
The craft is in making a tube of sausage carry a stack designed for flat slices. The frankfurter is griddled or boiled and seated in a soft split bun, and the Reuben components are layered over the top rather than sealed between bread, so the build is open and the bun has to be sturdier than a plain hot dog bun to take the weight. The sauerkraut is wrung out hard before it goes on, the same discipline a griddled Reuben demands, because a wet kraut floods a split bun from the inside and the bottom gives way. The Swiss is laid over the hot dog and the warm kraut so it slumps and binds the pile to the sausage instead of sliding off, and the Thousand Island is striped on last, supplying the sweet, tangy richness from the top. The bun is plain and soft and meant to disappear under the load, the carrier and not the point. It is assembled fast off a hot-dog line and eaten in hand, a deli sandwich's flavor in street-food form.
The variations are small swaps on a settled idea. Swapping Thousand Island for Russian dressing sharpens it; a Rachel dog runs coleslaw in place of the sauerkraut for a sweeter, milder reading; a brat or a smoked sausage in place of the frankfurter pushes it coarser and meatier. It descends from the griddled Reuben and sits beside the broader American hot dog and its dense regional dialect, and those relatives deserve their own articles rather than being crowded in here.