Add star anise, cloves, cardamom, and cinnamon sticks to a large soup pot and toast over medium heat for 5 minutes or until fragrant.
Add broth, brown sugar, soy sauce, vinegar, salt, onion, and ginger. Cook over medium-low heat for 30 minutes.
Add oil to a frying pan and place over medium-high heat.
Add mushrooms and cook for 5 minutes, stirring frequently. Set aside.
Cook noodles according to package instructions.
Using a slotted spoon, remove and discard the star anise, cloves, cardamom, cinnamon sticks, onion, and ginger from the soup pot. Keep the broth warm over medium heat.
Add the cooked mushrooms, carrots, and bok choy leaves to the broth to warm through.
Divide noodles among bowls and ladle in the broth and vegetables.
Garnish the soup with scallions, basil, mint, and lime before serving.