Heat 1 teaspoon oil in a large nonstick skillet over medium heat. Add eggs; cook, stirring gently, until set, 2 to 3 minutes. Remove to a plate.
Wipe out the pan and heat the remaining 2 teaspoons oil over medium heat. Add ginger and garlic and cook, stirring, until softened and fragrant, 1 minute. Add shredded vegetables, bean sprouts, half the sliced scallions, soy sauce and vinegar. Stir to combine. Cover and cook, stirring once or twice, until the vegetables are just tender, about 3 minutes.
Add the reserved eggs and hoisin; cook, uncovered, stirring and breaking up the scrambled eggs, until heated through, 1 to 2 minutes. Stir in the remaining scallions and remove from the heat.