Heat olive oil in a large Dutch oven or heavy soup pot over medium-high heat. Add Italian sausage and cook for 5 to 6 minutes, breaking it up with a wooden spoon until browned and cooked through. Remove sausage with a slotted spoon to a plate, leaving about 1 tablespoon of drippings in the pot.

Add diced onion, carrots, and celery to the pot. Sauté over medium heat for 5 minutes until vegetables begin to soften. Stir in minced garlic and tomato paste, cooking for 1 minute until fragrant and deepened in color.

Pour in chicken broth, diced tomatoes with juices, and tomato sauce. Whisk gently to scrape up any browned flavorful bits from the bottom of the pot. Return browned sausage to the pot along with drained cannellini beans, kidney beans, Italian seasoning, fresh rosemary sprig, salt, and black pepper.

Bring soup to a gentle boil, then reduce heat to low, cover with lid, and simmer gently for 15 minutes to allow the rich flavors to meld together.

Stir in dry ditalini pasta. Simmer uncovered over medium-low heat for 9 to 10 minutes, stirring occasionally, until pasta is al dente. Remove and discard the rosemary sprig.

Ladle hot soup into wide shallow bowls. Top generously with freshly grated Pecorino Romano cheese, fresh chopped parsley, and a light drizzle of extra virgin olive oil. Serve immediately with warm toasted garlic bread.