Meanwhile, arrange a rack 6 to 8 inches below broiler element and pre-heat broiler to high. In a bowl, whisk together the miso, 2 tablespoons mirin, and fresh ginger. Slather the mushrooms, top and bottom, with the miso mixture. Place on a foil-lined rimmed baking sheet, and broil until tender and charred, turning once, about 20 minutes total. Set aside.