In a skillet, cook beef over medium-high heat until browned, 5 minutes. Add ginger and garlic during last 2 minutes.
Meanwhile, cook noodles according to package until al dente. Drain and set aside.
Drain excess fat from beef. Add brown sugar, broth, soy sauce, hoisin, black pepper, and red pepper flakes if using. Stir well.
In a small bowl, whisk together cornstarch and water to make a slurry. Pour into beef mixture and bring to a simmer until thickened, 2-3 minutes.
Add cooked noodles to the skillet and toss to coat evenly in the sauce. Allow to sit for 2-3 minutes so noodles absorb flavor.
Serve garnished with sliced green onions.