Cook noodles according to the instructions on the box. Drain, rinse with cold water, and set aside.
In a 12-inch skillet or wok, brown ground beef with 1 tablespoon of sesame oil until meat is no longer pink and is cooked through.
Add garlic paste and ginger paste to the skillet and brown for an additional minute.
Add chili paste, soy sauce, brown sugar, hoisin sauce, and ½ of the beef broth to the skillet.
Stir the cornstarch into the remaining ½ cup of broth until dissolved. Add the cornstarch/broth mixture to the skillet.
Saute over medium heat until sauce is bubbly and meat is evenly seasoned with the sauce.
Add ¼ to ½ cup of green onions sliced on the diagonal into 1-inch pieces. Taste the sauce and adjust seasoning to taste (add additional chili paste or red pepper for more spice, etc.).
Saute for 1 to 2 minutes longer.
Add the cooked noodles to the skillet and toss to coat with sauce.
Garnish with additional green onions and sesame seeds, if desired.