Cook the noodles (while you make the broth): Heat large pot of water to a boil and cook noodles to al dente. Drain and set aside. If necessary, refresh the noodles under some hot tap water before serving.
Make the broth: In a large pot or Dutch oven, heat the sesame oil and the olive oil over medium high heat. Add the onion and cook for 4 minutes until lightly browned on the edges. Add the garlic and cook for 30 seconds until just browned, stirring constantly. Add the vegetable broth and bring to a simmer.
Add the mushrooms, carrots, 3 tablespoons miso paste and mirin and cook for about 10 minutes until the mushrooms are tender. Add the soy sauce, coconut milk (for creamy broth), green onions, cabbage, spinach and cook until the spinach is just wilted, about 1 minute. Taste and add about 1 tablespoon more miso paste to taste.
Serve: To serve, place the noodles into four bowls. Top with broth, eggs, and vegetables. Store leftovers with the broth and noodles in separate containers (to avoid the noodles soaking up all of the broth).