1. Cook the ramen noodles according to the package instructions. Drain and set aside, discarding the flavor packets.

2. In a large skillet over medium-high heat, heat the vegetable oil. Toss the sliced steak with the cornstarch until evenly coated, then sear the beef for about 2 minutes per side, or until nicely browned. Remove the beef from the skillet and set it aside.

3. Reduce the heat to medium-low and add the sesame oil to the skillet. Sauté the garlic and ginger for about 1 minute, or until fragrant. Stir in the soy sauce, brown sugar, and broth, bringing the mixture to a gentle simmer. Allow the sauce to thicken slightly.

4. Add the broccoli and carrots to the skillet, cover, and steam for about 5 minutes, or until the vegetables are tender-crisp.

5. Return the seared beef to the skillet, along with the cooked ramen noodles and sliced scallions. Toss everything together, ensuring the sauce coats the noodles, beef, and vegetables evenly.

6. Sprinkle the Mongolian Beef Stir-Fry with Ramen with toasted sesame seeds and serve immediately, while hot and fragrant.