Cook noodles according to package instructions. Drain and set aside.
In a large skillet or wok, heat vegetable oil over medium-high heat. Add ground beef and cook until browned and cooked through, breaking it apart with a spoon as it cooks.
Add minced garlic and grated ginger to the skillet with the beef and cook for an additional 1-2 minutes, until fragrant.
In a small bowl, whisk together soy sauce, water, brown sugar, rice vinegar, sesame oil, and cornstarch until smooth.
Pour the sauce mixture over the beef in the skillet. Stir well to combine.
Add cooked noodles to the skillet and toss until evenly coated in the sauce.
If desired, add sliced vegetables to the skillet and cook for an additional 2-3 minutes, until vegetables are tender-crisp.
Garnish with sliced green onions and sesame seeds before serving.