Cook the noodles and broccoli: Bring a large pot of salted water to a boil. Cook the noodles according to package instructions. Drain and toss with 1 teaspoon sesame oil, then set aside. Refill the pot with salted water and bring to a boil again. Add broccoli florets and cook for 4–5 minutes until tender but still crisp. Drain and set aside.
Cook the beef: Season the sliced flank steak with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add the beef bouillon cube, then add the steak. Cook until browned and no longer pink, about 3–4 minutes. Remove and cover with foil to keep warm.
Sauté aromatics and vegetables: Return the skillet to medium high heat. Add minced garlic and ginger, and cook for 1–2 minutes until fragrant.
Add bell pepper, water chestnuts, and shredded carrot. Cook for 3–5 minutes until slightly tender.
Make the sauce: In a bowl, whisk together brown sugar, soy sauce, hoisin sauce, sriracha, and sesame oil until smooth.
Combine everything: Add noodles, broccoli, and beef back into the skillet. Pour in the sauce and toss until evenly coated and heated through.
Serve: Garnish with sesame seeds and sliced green onions. Serve hot and enjoy!