In a medium bowl, whisk together soy sauce, brown sugar, water, sesame oil, and red pepper flakes until sugar dissolves completely.
Bring a large pot of water to a boil and cook noodles according to package directions, but subtract 1 minute from the recommended time. Drain and rinse with cold water to prevent sticking.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add ground beef, breaking it apart with a wooden spoon. Cook until beef is no longer pink, about 5-7 minutes.
Add minced garlic and grated ginger to the browned beef. Stir frequently for 30-60 seconds until fragrant but not browned.
Pour the prepared sauce into the skillet with beef and aromatics. Bring to a simmer and let it reduce for 2-3 minutes.
Add the drained noodles and toss to coat thoroughly. If the sauce seems too thin, add the cornstarch slurry and cook for an additional 1-2 minutes until thickened.
Fold in most of the sliced green onions, reserving some for garnish. Remove from heat and serve immediately, garnished with remaining green onions and optional sesame seeds.