In a large pot, combine the chicken broth, vegetable broth, miso paste, soy sauce, mirin, sesame oil, garlic, and ginger. Bring to a simmer over medium heat.
Add the sliced onion, carrot, and dried shiitake mushrooms to the pot. Simmer for 1-2 hours, until the broth is flavorful and the vegetables are tender.
While the broth is simmering, prepare the soft-boiled eggs and ramen noodles according to their package instructions.
Once the broth is ready, strain out the vegetables and mushrooms and return the broth to the pot. Keep warm.
Divide the cooked ramen noodles between two bowls. Ladle the hot broth over the noodles.
Top each bowl with roasted pork slices (chashu), nori seaweed, sesame seeds, sliced green onions, bean sprouts, and a drizzle of chili oil (if desired).
Serve the miso ramen hot and enjoy!