Make the Chili Dog Sauce: Heat the olive oil in a large skillet over medium-high heat. Add the ground beef and cook undisturbed for 3 minutes. Add the onions and continue cooking the ground beef, stirring and breaking it up, for 3 to 5 minutes or until no longer pink. Add chili powder, salt, pepper, garlic powder, celery seeds, cumin, cinnamon, allspice, cayenne pepper, tomato paste, and 1 cup of water. Bring to a boil. Reduce heat and simmer for 1 to 2 hours or the meat is tender and almost paste-like. Use a potato masher, blender, or immersion blender to process the meat.

Assemble the Coney Island Hot Dogs: Put the hot dogs in the prepared buns and top with about 2 to 3 tablespoons of sauce. Sprinkle a tablespoon or two of chopped onion over the ground beef mixture then drizzle mustard over the length of the hot dog.