Cook the wide rice noodles according to package instructions; drain, rinse under cold water, and set aside.
Heat a 12-inch skillet or wok over medium-high heat and add 1 tablespoon sesame oil. Add the ground beef and cook, breaking up with a spatula, until no longer pink.
Add the garlic paste and ginger paste to the skillet and cook for about 1 minute until fragrant.
Pour in the chili paste, light soy sauce, light brown sugar, hoisin sauce, and half of the beef broth (1/2 cup). Stir to combine.
In a small bowl, whisk the cornstarch into the remaining 1/2 cup beef broth until dissolved, then add this slurry to the skillet.
Sauté over medium heat until the sauce becomes bubbly and thickens, coating the beef evenly, about 1–2 minutes. Add red pepper flakes if you want more heat.
Stir in 1/4 to 1/2 cup of the sliced green onions and cook for 1–2 minutes more to soften slightly.
Add the cooked rice noodles to the skillet and toss thoroughly to coat with the sauce and combine with the beef.
Serve immediately, garnished with remaining green onions and sesame seeds if desired.