Add the soy sauce, mirin, and sugar into a saucepan and cook over medium-low heat. As the mixture begins to boil, reduce the temperature to a simmer. Continue to cook for 15-20 minutes. Remove from heat and set aside.
Thread an even amount of mushrooms and pieces of scallion onto each skewer, Brush the mushrooms and scallions with a light layer of EVOO.
Place the skewers in a sauté pan with a tablespoon of EVOO over medium-high heat. Cook the skewers for about 4-6 minutes or until the mushrooms are tender and throughly cooked.
Remove from heat, and with a pastry brush, baste them with the sauce. You can serve the skewers as is or remove them from the skewers and serve family style.
*If you are using wooden skewers be sure to soak them in water for at least 10 minutes before cooking.