In a skillet, cook the ground beef over medium-high heat until browned, about 5 minutes. Add grated ginger and minced garlic in the last 2 minutes of cooking.
Cook noodles according to package instructions until al dente. Drain and set aside.
Drain excess fat from the skillet. Add brown sugar, beef broth, soy sauce, hoisin sauce, black pepper, and red pepper flakes (if using). Stir well to combine.
In a small bowl, whisk together cornstarch and water to form a slurry. Pour into the skillet with beef and bring to a simmer, stirring until the sauce thickens, about 2-3 minutes.
Add cooked noodles to the skillet and toss to coat evenly with the sauce. Allow to sit for 2-3 minutes for the noodles to absorb the flavors.
Serve the noodles garnished with sliced green onions.