Add olive oil to a large Dutch oven over medium-high heat, then add the onion, carrots and celery and cook until softened, about 7-10 minutes. Add the garlic and cook until fragrant, about 1-2 minutes more. Add the Italian sausage and cook until no longer pink, breaking meat up into small pieces as it cooks, about 5 minutes.
Add the remaining ingredients except for the ditalini pasta and let simmer, covered, for a minimum of 20 minutes.
While soup simmers, cook ditalini pasta in a separate pot, following the instructions on the box. Drain well and set aside. When ready to serve, scoop ½ cup of cooked pasta into a bowl, then top with the soup. Garnish with parmesan and enjoy!