Cook the noodles according to the package instructions. Drain and set aside.
In a small bowl, whisk together the soy sauce, brown sugar, hoisin sauce, red pepper flakes (if using), water, and cornstarch. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the ground beef and cook until browned, breaking it into crumbles as it cooks. Drain any excess grease.
Add the minced garlic and grated ginger to the beef and cook for 1–2 minutes, until fragrant.
Pour the sauce mixture into the skillet with the beef. Stir well and bring to a simmer. Cook for 2–3 minutes, allowing the sauce to thicken slightly.
Add the cooked noodles to the skillet, tossing to coat them in the sauce. Stir in the chopped green onions and cook for another 1–2 minutes, until everything is heated through.
Serve immediately, garnished with sesame seeds and additional green onions if desired.