In a large skillet, heat the oil over medium-high heat. Once it's hot, add the sausage and cook until its browned throughout, breaking it up as you go. Once its browned, place it on a towel lined plate to drain off some of the grease and set it aside.
Grease your slow cooker, then add the sausage, onion, celery, carrot, garlic, rinsed beans, crushed tomatoes, broth and seasonings. Give it all a good stir, then pop the lid on and set the heat to low for 5-6 hours.
Once the soup is ready to eat, heat a large pot of salted water to a boil. Cook the ditalini pasta according to package directions, then drain and stir it along with the 1/2 cup grated parmesan into the soup. Then taste the soup and add any additional seasonings you think it needs. That's it!
