Cover the noodles with hot water in a large bowl and place a small plate on top to keep them submerged; set aside to soak for 5 minutes. Drain the noodles well and set aside. Discard the flavor pouches or reserve for another use.
Cut the beef crosswise into 2- to 3-inch pieces and then rotate a quarter turn and slice thinly lengthwise across the grain, about 1/4-inch thick.
Stir together the chicken broth, teriyaki sauce, cornstarch, sugar and sesame oil in a small bowl or measuring cup and set aside.
Heat 1 tablespoon of the vegetable oil in a wok or a large nonstick skillet over high heat until lightly smoking. Add half of the beef and cook, stirring once, until brown on the outside and still juicy on the inside, 1 to 2 minutes. Remove with a slotted spoon to a large bowl. Repeat with an additional 1 tablespoon vegetable oil and the remaining beef.
Heat 1 tablespoon vegetable oil in the same skillet over high heat. Add the broccoli and cook, stirring frequently, until the broccoli just starts to soften, about 1 minute. Reduce the heat to medium and push the broccoli to the side. Add 1 teaspoon vegetable oil, the ginger and garlic and cook, stirring, until fragrant, about 30 seconds. Add 1/4 cup water to the skillet and cook, stirring occasionally, until mostly evaporated, about 1 minute. Stir the chicken broth mixture briefly and add it to the skillet. Bring to a boil and cook, stirring occasionally, until thickened, about 1 minute. Add the beef and stir to coat. Transfer the beef to a large serving platter, leaving room for the noodles.
Wipe out the skillet and heat the remaining 2 tablespoons vegetable oil over medium-high heat. Add the ramen noodles and scallions and cook, stirring frequently, until heated through, about 1 minute. Transfer to the serving platter and garnish with additional scallions, if desired. Garnish the beef with toasted sesame seeds and serve.
Cook's Note: If you have extra time and want to cut your skirt steak very thinly, cut the steak into 4 pieces and freeze for 30 minutes before slicing. Cook until just seared and still juicy inside, about 1 minute per batch.