Combine the yam, 2 tablespoons soy sauce, 1/4 cup mirin, and sugar in a small saucepan with about 1/2 cup water. Cover and cook over medium heat until the yam is tender, about 15 minutes, adding a little more water if necessary.
Uncover and cook, stirring occasionally, until the yam pieces are glazed and the mixture is almost dry. Add the remaining teaspoon of soy sauce and mirin, cook for another 5 seconds, and serve.
