Prepare the Dipping Sauce: In a small bowl, mix soy sauce, rice vinegar, sesame oil, grated ginger, sugar, and green onion. Set aside for flavors to meld.
Prepare the Tempura Batter: In a mixing bowl, whisk the egg lightly, then gently stir in ice-cold water. Gradually add flour, cornstarch, and salt. Stir lightly—lumps are okay! Overmixing can make the batter heavy.
Heat the Oil: Heat vegetable oil in a deep pan to 350°F (175°C). Use enough oil to submerge the mushrooms.
Coat the Mushrooms: Pat mushrooms dry, then dip them into the batter, ensuring an even coat.
Fry to Perfection: Fry mushrooms in small batches until golden and crisp, about 2–3 minutes per batch. Drain on paper towels.
Serve: Arrange crispy mushrooms on a platter and serve hot with the prepared soy dipping sauce.