In a medium saucepan bring the chicken or vegetable broth to a low boil. Reduce heat to medium low and add the star anise and cinnamon stick. Allow the broth and spices to simmer, covered, for approximately 10 minutes to infuse the flavors of the spices into the broth. When finished, remove spices with a slotted spoon.
With the broth still simmering on low, gently crack the eggs, one-by-one into the simmering soup. Cook the eggs for two minutes before (very!) carefully add the noodles, bok choy, green onion and snap peas. Simmer everything together for 2-3 minutes and add the soy sauce and lime juice.
Remove from heat and taste. Add more soy sauce if needed. Divide the soup between two bowls and garnish with fresh cilantro and chili flakes. Best eaten immediately.