Melt coconut oil in a large saucepan over medium heat. Add cabbage, onion, mushrooms, red pepper and a pinch of salt. Sauté about 5 minutes, until vegetables begin to soften. Stir in ginger.
Add vegetable stock, cover, and bring to a simmer. Simmer about 10 minutes, until vegetables are tender.
Meanwhile, bring a medium pot of water to boil. Add noodles, and cook for 1 minute. When noodles begin to unfold, separate with a fork and reduce heat to a low boil. Simmer 3–4 minutes, until soft. Strain, and rinse with cold water.
Add noodles to soup, and stir in steak, carrots, tamari, lime juice and salt. Cook steak about 2 minutes, until no longer pink. Season to taste. Garnish with scallions and red pepper flakes.