Bring a large pot of salted water to a boil. Add pasta and cook according to package directions for al dente. Drain, reserving 2 cups cooking water.
In same pot, heat oil over medium. Add sausage; cook, breaking it up using a spoon, until lightly browned, 3 to 4 minutes. Add onion; cook, stirring occasionally, until sausage is well browned and onion is softened, 3 to 5 minutes.
Add chickpeas and tomato paste to pot; cook, stirring often, until tomato paste begins to caramelize, 2 to 3 minutes. Add reserved cooking water and salt; bring to a simmer over medium-high. Cook, stirring often and scraping up browned bits from bottom of pot, until slightly thickened, about 3 minutes.
Remove pot from heat and stir in pasta. Serve topped with cheese. Garnish with parsley (if desired) and drizzle with oil.
