In a large, deep pot over medium heat, heat oil. Add sausage and cook, breaking up with a wooden spoon, until cooked through, about 5 minutes. Stir in onion, carrots, and celery and cook until slightly softened, about 5 minutes.
Add garlic and cook until fragrant, 1 minute more. Season with salt and pepper, then add in beans (with their liquid), diced tomatoes, chicken broth, and rosemary. Bring to a boil, then stir in ditalini.
Reduce heat to medium and cook until pasta is al dente, about 8 minutes. Taste and adjust seasoning if necessary.
Serve in bowls garnished with Parmesan and parsley.
Recipe by 5* trending recipes with videos at https://food.theffeed.com/2020/05/02/pasta-e-fagioli/