In a small bowl, whisk together hoisin sauce, soy sauce, sesame oil, minced garlic, grated ginger, and beef broth. Set aside.
In another small bowl, whisk cornstarch with 2 tablespoons of water until smooth. Add this slurry to the hoisin sauce mixture and stir well. This will be your sauce.
Cook egg noodles according to package directions. Drain and set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add sliced beef and stir-fry until browned. Remove beef from skillet and set aside.
Add broccoli florets and sliced carrots to the same skillet. Stir-fry for 3-4 minutes until vegetables are tender-crisp.
Return the cooked beef to the skillet with the vegetables. Pour the prepared hoisin sauce mixture over everything. Stir well to coat.
Simmer for 2-3 minutes, stirring occasionally, until the sauce has thickened. If the sauce is too thick, add a splash more beef broth.
Add the cooked egg noodles to the skillet and toss to combine with the beef and vegetables. Ensure noodles are well coated with the sauce.
Serve immediately, garnished with sesame seeds and sliced green onions.
Notes
This recipe is easily adaptable. Feel free to add other vegetables like bell peppers or snap peas.