To a large pot set over medium-high heat, add the oil; when the oil is hot, add the celery, carrot, onion, and rosemary and cook, stirring occasionally, until the vegetables are softened, 8–10 minutes. Add the stock and chickpeas, bring to a simmer, and cook for 5 minutes. Using a slotted spoon or spider skimmer, transfer about half of the chickpea-vegetable mixture to a blender or food processor and puree until smooth. Return the puree to the pan, then add the cavatelli and continue cooking until the pasta is al dente, about 10 minutes. Season to taste with additional salt and pepper as needed, stir in the parsley, and garnish with parmesan cheese.
