Cook the buckwheat noodles according to the packet instructions. Drain and set aside.
Slice the onion and garlic, and cut the carrot into thin strips. Halve any large shiitake mushrooms.
Heat the oil in a large pan and cook the onion for about 5 minutes until softened.
Add the garlic, mushrooms, and carrot. Stir briefly, then add the soy sauce, rice vinegar, and mirin.
Cover and cook for about 5 minutes, until the vegetables start to soften.
Add a small glass of water, then the green beans.
Place the salmon fillets on top of the vegetables and drizzle with sesame oil. Cover and steam for 5–8 minutes, depending on thickness, until just cooked.
Divide the noodles between plates, then top with the vegetables and salmon.
Finish with sesame seeds and chopped coriander.