In a large pot with boiling water, cook the noodles according to package directions. Add the broccoli the last 5 minutes of cooking and let them cook until tender. Drain the noodles and broccoli.
While the pasta is cooking, add olive oil to a medium sized skillet. Cook the steak until no longer pink. Add the garlic, and carrots and cook for a minute more.
In a small bowl whisk together the brown sugar, soy sauce, hoisin sauce, sesame oil, ginger, red pepper and pepper.
Add the spaghetti to the skillet and pour the sauce on top and toss until incorporated.