Place chicken broth, garlic, ginger slices, and star anise (if using) in a large saucepan. Bring to a simmer over high heat, then reduce to the lowest heat and simmer gently for 10 minutes to infuse flavors.
Turn heat up to high and bring liquid to a rapid simmer. Add carrot slices and Chinese broccoli stems. Cook for 3 minutes.
Add Chinese broccoli leaves, push into the simmer for 2 minutes until just wilted.
Remove and discard the garlic and ginger slices.
Stir in the light soy sauce, sugar, Chinese cooking wine, and toasted sesame oil (if using).
Ladle the soup into two bowls. Serve immediately and enjoy this healthy, quick meal!