In a large soup pot or dutch oven over medium heat, heat the olive oil. Add the onion, carrot, and celery and cook until vegetables are softened, about 10 minutes. Stir in the tomato and cook a few minutes more. Season with a generous sprinkling of salt.
Add 2 cups chickpeas and the water and bring to a boil, then simmer for about 15 minutes. In a blender or using an immersion blender, carefully puree the soup. Return to the pot and add the pasta; cook until al dente.
Stir in the remaining ½ cup of the chickpeas and the parsley if using. Salt and pepper to taste. Finish with parmesan if desired. Soup can be stored in an air-tight glass container in the fridge for 3 days.