Cook noodles according to package instructions, drain and toss with sesame oil to prevent sticking. Set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Add ground beef and cook until browned, breaking it apart, then drain excess fat.
Add chopped onion and cook until softened.
Stir in minced garlic, ginger, and the white parts of the green onions; sauté for one minute.
Add shredded carrots and sliced bell pepper; stir-fry for 2 to 3 minutes until slightly tender but crisp.
Whisk together all sauce ingredients in a bowl and pour into the skillet.
Add cooked noodles to skillet and toss to evenly coat and heat through, about 2 to 3 minutes.
Garnish with sesame seeds, green onion tops, and a drizzle of chili oil or Sriracha if desired. Serve hot.