Break stem off chilis and shake out seeds. In a small bowl cover the chilis with hot water and let stand until softened, 5 to 10 minutes. Drain and coarsely chop.
Pour olive oil into a 12 inch nonstick sauté pan over medium-low heat. Add pasta; stir and turn often with tongs until almost golden, 3 to 5 minutes. Stir in the anise, cumin seeds, onion and garlic. Slowly lift the pasta, with tongs, so it mostly sits on top of onion mixture., and then cook onion mixture, stirring often, until softened, 4 to 5 minutes. .
Stir in chilis and chicken broth. Bring it to a simmer over high heat, then reduce heat to medium and simmer for 3 minutes; add shrimp and simmer until pasta is tender to the bite, 3 to 4 minutes. Add more liquid (water or broth if needed). Season the soup with salt and pepper to taste.
Spoon the soup into wide, shallow bowls. Top each serving with a spoonful of sour cream, avocado, and sprinkle with cilantro.