For the short ribs, trim out most of the fat. Make 2 – 3 slits in each piece of meat, which will help the meat to absorb the flavors easier. Soak the meat in a large bowl of cold water for 1 – 2 hours to remove blood.
Rinse the short ribs under cold water. Transfer to a large pot and fill enough water to cover the ribs. Bring to a boil over high heat. Drain and rinse the ribs with cold water for 3 times. Drain and set aside.
In another large pot, add 3½ cups water, soy sauce, sugar and honey. Mix well. Add the short ribs. Cook over medium heat with a lid for 20 minutes. Add onion, green onion, garlic and black pepper. Turn the heat to medium-low. Boil with a lid for 1 hour.
For the potatoes and carrots, peel and rinse. Cut into 1-inch cubes. Add to the pot. Cover partially with a lid and cook until the potatoes are just tender, about 30 minutes.
Meanwhile, if using rice cake, bring a medium pot of water to a boil over high heat. Once boiling, add the rice cake. Cook for about 6 - 7 minutes. Drain and add to the pot of beef.
In a small heatproof bowl, add ¼ cup of hot cooking liquid and 1½ tablespoons gochujang. Stir to mix well. Return the mixture to the pot. Taste and adjust with more gochujang if desired. Cook without a lid for another 4 - 5 minutes.
If desired, remove some of the oil on top with a large spoon.
Transfer the meat, potatoes, carrot, and rice cakes to a large serving bowl. Spoon desired amount of sauce over. Sprinkle with green onion and sesame seeds. Serve with steamed rice and kimchi.