Combine the chickpeas with the olive oil, garlic, rosemary, and tomatoes in a heavy 6-quart soup pot or Dutch oven with 8 cups of cold water; bring to a boil over medium-high heat. Reduce heat to medium-low; simmer, uncovered, about 30 minutes.
Pass half the chickpeas through a food mill, or puree in a food processor or blender (or use an immersion blender in the pot); return the puree to the soup.
Add the pasta and continue cooking until the pasta is al dente, 10 to 12 minutes.
Season to taste with salt and pepper. Add a drizzle of olive oil to each serving.