Bring a large pot of salted water to a boil over high heat. Add the beans and carrots and cook for 1 minute. Drain and put in a bowl of iced water until cool, about 1 minute. Drain and set aside.
Return the water to a boil. Add the noodles and cook, stirring occasionally, until tender, about 5 to 7 minutes. Drain and rinse with cold water. Pat dry and set aside.
In a large nonstick skillet, heat the oil over high heat. Add the noodles, ginger and garlic. Cook for 2 minutes until the noodles are lightly browned. Add the mushrooms, beans, carrots, and water chestnuts and cook for 3 minutes. Add the broth, hoisin sauce, soy sauce, and honey. Bring the mixture to a boil and stir until slightly reduced and thick, about 2 minutes. Season with salt and pepper, to taste.
Transfer the chow mein to a large bowl and garnish with the green onions before serving.
*Can be found at specialty Asian markets.