In a skillet over medium-high heat, cook the ground beef until browned (about 5 minutes). Add minced garlic and grated ginger during the last 2 minutes.
Meanwhile, boil water in a pot and cook noodles according to package instructions until al dente. Drain and set aside.
After draining excess fat from the beef, add brown sugar, beef broth, soy sauce, hoisin sauce, black pepper, and red pepper flakes (if using). Stir well.
In a small bowl, whisk cornstarch with water until smooth. Pour into the skillet with the beef sauce and simmer for 2-3 minutes until thickened.
Toss cooked noodles into the skillet with the beef mixture and stir gently to coat evenly.
Serve hot garnished with sliced green onions.
