Make the broth by boiling all the ingredients for it in a small pot over medium high heat for 10 minutes. Strain the broth. You should end up with about 1 cup of broth. Do not season at this point.
In a medium sized pot, add the sesame oil and saute the pork, onion, kimchi, garlic, and red pepper flakes, stirring occasionally, until the kimchi and onions are softened, and the meat is cooked, about 3 minutes. Pour in the kimchi juice and broth. Bring to a boil and cook for a couple minutes. Add the fish sauce and season with salt and pepper as needed.
Slice through the package of tofu with your knife. Gently add the tofu and break it up with your spoon, making sure not to make the chunks too small. Since the tofu is delicate, there’s a possibility of it breaking up too much and disappearing if the pieces are too small. Bring to a boil again and cook for 5 minutes, stirring the bottom of the pot gently with a spoon occasionally, to make sure the tofu doesn’t burn. Taste one more time and adjust the seasoning if needed. Add the enoki mushrooms, scallions, and egg on top. Turn off the heat and serve with bowls of rice. The heat of the bubbling broth should be hot enough to cook the egg as you eat it.