Cover shiitake in a bowl with 2 cups hot water. Let stand for 20 minutes.
Add the soaking water to a saucepan with 6 cups water, buckwheat, 2 whole spring onions, ginger, star anise, mirin and tamari. Bring to the boil slowly and simmer for 20 minutes. Add the carrots and sliced shiitake (stems removed) and cook for a further 15 minutes. Remove ginger, shallots and star anise. Place into serving bowls and add 1 tsp chopped coriander and 1 tsp chopped shallots. Serve.
Note: Buckwheat can be substituted for buckwheat noodles if preferred and added in the last 5 minutes of cooking.