In a large pot, combine the water, dried anchovies, green onion, dried red chili, soup soy sauce, gochujang, garlic, gochugaru, and black pepper. Bring to a boil over high heat, then reduce the heat to medium and simmer for 15 minutes.
Strain the broth through a fine-mesh sieve, discarding the solids. Keep the seasoned broth warm on the stove.
In a small bowl, whisk together the soy sauce, rice vinegar, water, and wasabi paste to make the dipping sauce. Divide this mixture into four small individual bowls.
Arrange the sliced beef, shiitake mushrooms, king oyster mushrooms, napa cabbage, bok choy, and onion on large platters. Set up a portable burner in the center of your dining table.
Pour about half of the strained broth into a wide, shallow pot and place it on the portable burner over medium-high heat. Once the broth is boiling, diners can begin adding vegetables and dipping slices of beef into the broth to cook. Ensure the beef reaches a safe internal temperature of 145°F (63°C) and rests for 3 minutes before eating.
Dip the cooked meat and vegetables into the prepared sauce. Add more broth from the kitchen as the liquid in the pot evaporates.
When most of the meat and vegetables are eaten, add the fresh noodles to the remaining boiling broth. Cook for 5 to 8 minutes until tender, then divide the noodles among the diners.
Remove any leftover solids and leave just a thin layer of broth in the pot. Add the cooked rice, chopped kimchi, sesame oil, crumbled seaweed, and the egg. Stir vigorously over medium heat until the egg is fully cooked and reaches 160°F (71°C), about 3 minutes.
Press the rice mixture flat against the bottom of the pot. Lower the heat and let it cook undisturbed for 5 minutes to form a crispy crust. Serve the fried rice directly from the pot.