Bring the water to a rolling boil over high heat. Once the water is boiling, stir in the ramen noodles with only 1 seasoning packs, and return to a boil. Cook until the noodles are tender, stirring occasionally, about 3 minutes. Drain well in a colander set in the sink. Whisk the beef broth, peanut sauce, soy sauce, and ground ginger together in a bowl; set aside.
Heat 1 tablespoon olive oil in a large skillet. Stir in the steak; cook and stir until the steak is no longer pink, 3 to 5 minutes. Remove the meat from the pan and set aside. Heat the remaining 1 tablespoon olive oil in the same skillet. Stir in the carrot, celery, green onion, and bell pepper. Cook and stir until the vegetables begin to soften, about 2 minutes. Add cabbage, bean sprouts, and mushrooms. Stir in the sauce. Cover and cook until the vegetables are tender, about 3 minutes.
Toss in the cooked ramen noodles and steak. Season with salt and pepper, and serve in bowls.
