Brown ground beef in a large skillet, stirring until it crumbles; drain and keep warm.
Pour sesame oil in pan and heat till hot. Saute onion and next 4 ingredients in hot sesame oil until tender.
Combine cornstarch and beef broth, whisking until smooth.
Stir broth mixture, hoisin sauce, and soy sauce into onion mixture.
Bring to a boil, stirring constantly; boil, stirring constantly, 1 minute.
Stir in ground beef.
Toss with hot cooked pasta, and sprinkle with sliced green onions.
In a small bowl, whisk together the broth, soy sauce, hoisin sauce, sesame oil and cornstarch until combined.
In a large nonstick skillet, heat the olive oil over medium heat. Add the broccoli and stir fry for 4-5 minutes until it is bright green and tender crisp. If you like it more well cooked, continue cooking for a couple more minutes. Add the garlic and continue stir frying for another minute or so. Pour the sauce over top of the broccoli and stir well to coat the broccoli with the sauce. Simmer for a minute or two until the sauce is heated through. Serve immediately.