Heat 2 tablespoons oil in a wok over high heat. Add the garlic and ginger and cook, stirring, until fragrant, about 60 seconds.
Add the mushrooms and 3 tablespoons Sudachi Ponzu Sauce and stir fry for 5–7 minutes or until they have released their liquid and are starting to brown. Add the white part of the onions, the carrots, edamame, and peas. Stir fry for 1–2 minutes. Remove from the pan and set aside.
Heat remaining tablespoon of oil in wok over high heat. Add the rice, remaining 2 tablespoons of Sudachi Ponzu Sauce, and vinegar and stir fry for a few minutes until the rice starts to lightly brown. Add the mushroom mixture back into the wok along with half the green parts of the green onions and stir fry for another 1–2 minutes. Garnish with the remaining green portion of the onion.