Preheat the oven to 300°F.
Heat the oil over medium-high in a heavy-bottomed, oven-safe dutch oven. Add the short ribs fat side down first and cook, rotating until all sides are brown, about 4 minutes each side. If cooking in batches, drain browned short ribs on a plate lined with paper towels.
Lower heat to medium. Return all meat to the pot. Add the soy sauce and cook, stirring until most of the liquid has evaporated. (You want the soy sauce to caramelize, but not burn.) Add onion, garlic, and ginger and cook about 3 minutes. Add tomato paste and spices and cook for another 4 minutes, or until the tomato paste has caramelized slightly. Add beef broth, miso, and mirin and stir. If needed, add water until the meat is completely submerged.
Cover the pot and transfer to the oven. Cook 3 to 3 1/2 hours, or until the meat is falling off the bone tender.
Using tongs, gently remove the short ribs from the liquid and place in a medium bowl. Strain the cooking liquid into a large bowl using a fine mesh sieve. Discard the spent ginger, onion, et cetera, and return the liquid to the pot, followed by the beef. Clear space in the fridge and let the mixture cool, ideally overnight.
When ready to eat, remove the dutch oven from the fridge. Skim off some of the solidified fat from the pot and discard. Over medium heat with the lid slightly ajar, reheat the short ribs until at a bare simmer.
Meanwhile, preheat the oven to 375°F. Mince the shallot and set aside. Cut the bread into 6 inch lengths and butter. Place on a sheet tray and toast for several minutes, or until golden brown. Set aside.
Using tongs, pull short ribs from the au jus and place in a large bowl. Using kitchen shears, snip the meat into one inch chunks. Place cheese on one half of all four of the sandwich toasts and place back in the oven until bubbling.
Ladle the remaining au jus into four bowls and distribute chopped shallots into all four. Pile snipped short ribs and their juices between each set of sandwich toasts. Cut in half if desired, and serve immediately. If there is any left over, meat will keep well up to 4 days in the fridge.