Grind first 4 ingredients in processor to coarse paste, stopping occasionally to scrape sides.
Heat oil in large pot over medium heat. Add paste; sauté until aromatic, about 2 minutes. Add stock, 2 cups water, 4 tablespoons lime juice, lemongrass, and star anise; bring to boil. Reduce heat; cover and simmer 10 minutes. Remove star anise. Add carrots and next 4 ingredients; simmer 2 minutes. Add fish; cook until just opaque, stirring gently, about 3 minutes. Mix in cilantro and 2 tablespoons lime juice. Season with salt and pepper.
*Available at Asian markets and in the spice section of some supermarkets.