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In a frying pan on the stovetop, sautée the carrots, cabbage, green onion and mushrooms in the toasted sesame oil until they are soft
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While the veggies are frying, heat the broth in a large pot on the stove. (Make sure that the broth only comes to the middle of the pot, or else it will overflow once you add the other ingredients!)
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Add the soft, cooked vegetables (and optional chicken or shrimp) and soy sauce to the broth, and bring it almost to a boil. It should be steaming but not bubbling.
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Add the ramen noodles to the pot, and cook until they are al dente (slightly chewy!)
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Serve with a hard-boiled egg!