Heat about four cups of water with the 1 tsp. of salt.
Start heating the vegetable oil in a wok or frying pan.
In a small pan, heat together the soy sauce, mirin, sake, sugar and ginger. Cook over medium heat for three to five minutes or just until slightly thickened.
Meanwhile, while the sauce cooks and while waiting for the water to boil and the oil to heat up, cut the tofu into 1 and 1/2 inch cubes.
Cut the mushroom caps into fairly think slices or you can just halve or quarter them, whatever suits your fancy.
When the water boils, blanch the mushrooms for about two minutes. Scoop out and set aside.
When the oil is hot, fry the tofu cubes until golden. Scoop out and drain on paper towels.
Toss the mushrooms and tofu together.
Stir the sesame oil into the teriyaki sauce.
Pour the sauce over the tofu and mushrooms.
Garnish the tofu and mushrooms teriyaki with sliced scallions and serve right away.