Use a hand-spiralizer, mandolin, or julienne vegetable peeler to spiralize the zucchini and carrot. Set on a clean dishcloth to absorb excess moisture while preparing the other ingredients.
Heat a wok or large skillet over high heat with 1 tbsp of the oil. When hot, add the shallots and ginger and stir-fry for 2 to 3 minutes until fragrant. Toss in the mushrooms and stir-fry for another 2 minutes.
Transfer to a plate and add another 1 tbsp of the oil to the wok and stir-fry the garlic, spring onions, chives, long beans, and watermelon radish for 2 minutes. Transfer to the plate with the mushrooms.
With the remaining 1 tbsp of oil, stir-fry the zucchini noodles for 1 minute, then return the stir-fried veggies to the wok. Season with the oyster sauce, soy sauce, sugar, salt, and white pepper, tossing to coat everything evenly. Drizzle in the cornstarch slurry and stir-fry for 1 more minute. These are best served immediately.