Heat a wok or wide soup pot over high heat until very hot. Add the oil, followed by the pork belly, and stir-fry for 2 minutes (or until lightly browned and caramelized).
Add the mushrooms, and stir-fry for 2 minutes. Then add the onion, garlic, kimchi, and sugar, and cook for 3 minutes. Finally, add the gochujang and cook for another minute. Remove this mixture to a plate, and set aside.
To the wok or pot, add the dashi stock, chicken stock, beef bouillon paste and water, and kimchi juice. Mix well to deglaze the surface of the pan and ensure the bouillon paste is completely dissolved. Bring to a boil. Stir in the gochugaru, fish sauce, and sesame oil, reduce the heat to low, and cover.
Meanwhile, bring a large pot of water to a boil for the noodles. Cook the noodles according to package instructions, and divide between 3-4 bowls. Cover with the broth, and top with the kimchi, pork belly, and mushroom mixture. Garnish with chopped scallions, and enjoy!