Add dashi stock, sake, and sugar into the pot. Place a drop lid and cook over medium heat until vegetables are soft.
In the meantime, prepare the snow peas. Remove the string, and quickly boil with a bit of salt. Remove from the heat and add them to cold water so the green color remains bright. Cut in half to make an arrow and a diamond shape.
Once vegetables in the pot are soft, remove the drop lid and add soy sauce, mirin, and salt. Place chicken on top and place the drop lid again. Cook over low heat until soup is almost gone. Stir occasionally.