Bring a large pot of water to a boil. Cook noodles according to package directions until just tender. Drain and set aside.
Heat sesame oil in a large skillet over medium heat. Add the ground beef and cook, breaking it up as it browns, about 6–8 minutes. Drain excess fat if needed.
Stir in the garlic and ginger, cooking for 1 minute until fragrant.
In a small bowl, whisk together soy sauce, brown sugar, water, hoisin, and red pepper flakes. Pour the sauce into the skillet with the beef and stir to coat.
If desired, mix 1 tbsp cornstarch with 1 tbsp water and stir it into the skillet. Simmer for 1–2 minutes until the sauce thickens.
Add the drained noodles to the skillet and toss everything together until the noodles are well coated in the sauce.
Sprinkle with green onions and sesame seeds. Serve hot straight from the pan.
