Marinate the beef: In a mixing bowl, combine soy sauce, sugar, minced garlic, grated ginger, and black pepper. Place the beef short ribs in the marinade, making sure they are well coated. Cover the bowl and refrigerate for at least 1 hour, or preferably overnight, to allow the flavors to penetrate the meat.
Prepare the vegetables: Peel and slice the carrots, peel and cut the potatoes into chunks, and slice the onion.
Cooking: Heat a large pot or Dutch oven over medium heat. Add the marinated beef short ribs (along with the marinade), sliced onions, carrots, and potatoes to the pot. Pour in water or beef broth until the ingredients are just covered.
Simmer: Bring the mixture to a boil, then reduce the heat to low. Cover the pot and simmer for 1.5 to 2 hours, or until the beef is tender and the sauce has thickened, stirring occasionally.
Finish: Once the beef is tender and the sauce has thickened to your liking, drizzle sesame oil over the top and give it a gentle stir to incorporate.
Serve: Transfer the galbi jjim to a serving platter or individual bowls. Garnish with chopped green onions and sesame seeds if desired. Serve hot with steamed rice and other side dishes.