If the sweet peppers are large, cut them in half diagonally. Break the maitake mushrooms into bite-sized pieces.

Heat sesame oil in a small frying pan and add the sweet peppers. Stir-fry over medium heat, turning them until they are browned all over.

Add the maitake mushrooms to the pan and stir-fry until the mushrooms are coated with oil. Add the simmering sauce ingredients, reduce to low heat, and cook until the liquid is absorbed.