Fill a large nonstick skillet with water and bring to a boil. Add the noodles and cook, stirring frequently, until just tender, 4-6 minutes or according to the package directions. Drain, rinse with cold water, and transfer to a large bowl. Wipe the pan dry.
Combine the Shao Hsing, black bean-garlic sauce, soy sauce, brown sugar, and cornstarch in a small bowl; set aside.
Heat 2 teaspoons of oil in the skillet over medium-high heat. Reduce the heat to medium. Add the ginger and cook, stirring, for 30 seconds. Add the onion and cook, stirring, until softened, 1-3 minutes. Add the vegetables and 1/4 cup water; cover and cook, stirring occasionally, until the vegetables are tender-crisp, 2-4 minutes. Transfer the vegetables to the bowl with the noodles. Wipe the pan dry.
Heat the remaining 2 teaspoons of oil in the skillet over medium-high heat. Add the steak and cook, stirring, until browned, 1-3 minutes. Stir the reserved sauce and add to the pan; cook, stirring, until the sauce has thickened slightly, 1-2 minutes.
Return the noodles and vegetables to the pan along with the remaining 1/4 cup of water; cook, tossing to coat with the sauce, until heated through, about 2 minutes more.
