Bring the dashi, mirin, soy sauce, and sugar to a boil in a pot.

Cut the napa cabbage and tofu into bite-sized pieces. Trim the stems from the mushrooms.

Boil the shirataki noodles briefly to remove any odor, then cut into easy-to-eat lengths. Soak the dried wheat gluten in water, then squeeze out the excess water.

Layer the beef, vegetables, mushrooms, tofu, shirataki noodles, and wheat gluten in the pot. Simmer until everything is cooked through.

Serve the sukiyaki-style simmered dish in bowls. Top each serving with a soft-cooked egg and sprinkle with green onions.