For the Braised Short Ribs: Preheat the oven to 325 degrees F (165 degrees C).
Season the beef pieces with some salt and pepper. Dredge the beef lightly with the flour and shake off excess; set aside. Heat 1 tablespoon butter and 1 tablespoon vegetable oil in a roasting pan over medium-high heat. Brown the short rib pieces on all sides, about 10 minutes. Use more butter and oil as needed to give a golden brown and delicious surface to each piece of beef.
Melt another tablespoon of butter in the pan. Stir in the shallots, carrots, and celery. Cook and stir until the vegetables have softened, about 10 minutes. Add the red wine, scrape up the brown bits in the pan, and reduce the wine volume by half. Stir in the beef broth, bay leaves, parsley and thyme. Add beef broth up to half the height of the contents of the pot, do not submerge. Bring the pot to a boil, cover with a tight fitting lid or aluminum foil, then transfer to the preheated oven until the short rib is very tender, about 2 1/2 to 3 hours. Once the short rib is tender, remove from the oven and allow to cool slightly. Strip the meat with a fork, cover and keep warm for the assembly stage.
For the Korean Taco Sauce: Whisk the soy sauce, sugar, gochujang and sesame oil together until the sugar has dissolved and the mixture is smooth. You can make this a few days in advance and store tightly covered in the refrigerator.
To Assemble the Tacos: Heat some tortillas in a dry skillet. In the same pan, add the vegetable oil, then briefly saute the Brussels sprouts, chopped onions and some salt and pepper. Add some shredded short rib and Korean Taco Sauce. Do not overcook.
Spoon some of the taco filling into each tortilla. Serve with the Korean Taco Sauce and a lime wedge.