Bring a large pot of salted water to a boil and cook the noodles according to the package instructions until al dente. During the final five minutes of boiling, toss in the broccoli florets so they can become tender yet retain a slight crunch. Once done, drain the noodles and broccoli and set aside.

Prepare the beef by slicing the flank steak into thin 1/4-inch strips, making sure to cut against the grain for optimal tenderness.

While the noodles are cooking, heat the olive oil in a medium skillet over medium-high heat. Add the sliced steak and sauté until it is browned and cooked through, with no pink remaining.

Stir in the minced garlic and shredded carrot, cooking for an additional minute to release the garlic’s aroma and slightly soften the carrot.

In a separate bowl, combine the brown sugar, soy sauce, hoisin sauce, sesame oil, ground ginger, crushed red pepper flakes, and black pepper. Whisk thoroughly to create a rich, savory-sweet sauce.

Add the cooked noodles and broccoli to the skillet with the beef and vegetables. Pour the sauce over the mixture, tossing everything together until well-coated and heated through.

Serve hot, garnished with chopped green onions and a sprinkle of sesame seeds for added flavor and texture.