In a large mixing bowl, combine garlic, black pepper, cornstarch, and 1 teaspoon vegetable oil. Add beef, and mix well.
In a large wok, heat 2 tablespoons oil over high heat for one minute. Add meat; cook and stir for about 2 minutes, or until beef begins to brown. Transfer beef to a large bowl, and set aside.
Heat 1 tablespoon oil in wok. Add onion; cook and stir until tender. Mix in green beans, and add broth. Cover, and reduce heat to medium. Simmer for 4 to 5 minutes, or until beans are tender crisp. Stir in fish sauce and beef. Cook, stirring constantly, for 1 or 2 minutes, or until heated through.