Boil noodles according to package directions. Drain, rinse lightly, and set aside.
In a large skillet, heat sesame oil over medium-high heat. Add ground beef and cook until browned, breaking it apart as it cooks. Drain excess grease if necessary.
Stir in minced garlic, ginger, and red pepper flakes (if using). Cook for 30 seconds until fragrant.
Pour in soy sauce and add brown sugar. Stir well, letting the sugar dissolve and the sauce begin to bubble.
If you want a thicker glaze: Mix cornstarch and water in a small bowl, then stir it into the skillet. Simmer for 1–2 minutes until thickened.
Add cooked noodles to the skillet and toss until everything is well coated in the Mongolian sauce.
Top with sliced green onions and serve hot.
