Break stems off chiles and shake out seeds. In a small bowl, cover chiles with hot water and let stand until softened, 5 to 10 minutes. Drain and coarsely chop.
Meanwhile, pour olive oil into a 12-in. nonstick frying pan over medium-low heat. Add pasta; stir and turn often with tongs until almost golden, 3 to 5 minutes. Stir in anise and cumin seeds, onion, and garlic. Lift pasta so it mostly sits on top of onion mixture, then cook onion mixture, stirring often, until softened, 4 to 5 minutes.
Stir in chiles and chicken broth. Bring to a simmer over high heat, then reduce heat to medium and simmer, 3 minutes; add shrimp and simmer until pasta is tender to the bite, 3 to 4 minutes more. Season to taste with salt.
Spoon soup into wide, shallow bowls. Top each serving with a spoonful of sour cream and some avocado, if you like, and sprinkle with cilantro.
How Hot Is Your Chile? To assess a chile's heat, slice off its top through the ribs and seeds, where the heat-producing compound capsaicin is concentrated. Touch the slice to your tongue. If you want your food to be milder, split the chile and scrape out all or some of the ribs and seeds. If your skin is sensitive, wear kitchen gloves or hold the chiles with a fork—and don't touch your eyes.
Note: Nutritional analysis is per serving.