In a large Dutch oven or heavy-bottomed pot, heat the olive oil over medium-high heat. Add the ground Italian sausage and cook, breaking it apart with a spoon, until it's browned and cooked through, about 5-7 minutes. Use a slotted spoon to transfer the sausage to a plate, leaving the rendered fat in the pot.

Add the diced onion, carrots, and celery to the pot. Cook, stirring occasionally, until the vegetables have softened, about 6-8 minutes. Add the minced garlic, dried oregano, dried thyme, and red pepper flakes. Cook for another minute until fragrant.

Pour in a splash of the chicken broth and scrape up any browned bits from the bottom of the pot. Add the rest of the chicken broth, the diced tomatoes (with their juice), the cooked sausage, the rinsed cannellini beans, and the Parmesan rind (if using). Stir everything together.

Bring the soup to a boil, then reduce the heat to low, cover, and let it simmer for at least 20 minutes to allow the flavors to meld together.

Remove the pot from the heat and discard the Parmesan rind. If making a creamy version, stir in the heavy cream. Season with salt and black pepper to taste. Ladle the hot soup into bowls and garnish with freshly grated Parmesan cheese and chopped fresh parsley.