In a large, heavy-bottomed pot, heat the olive oil over medium heat until shimmering.
Add the Italian sausage to the pot. Use a wooden spoon to crumble the sausage into smaller pieces as it cooks. Brown the sausage thoroughly, approximately 5-7 minutes, until it develops a golden crust.
Once the sausage is nicely browned, stir in the diced onion, carrots, and celery. Sauté these aromatic vegetables for about 5 minutes, or until they soften and the onion becomes translucent, releasing their natural sweetness.
Add the minced garlic to the pot and sauté for an additional 1 minute, until fragrant.
Carefully pour in the broth and add the drained white beans and diced tomatoes (with their liquid). Sprinkle in the dried oregano and thyme, then stir everything together to combine.
Increase the heat slightly and bring the soup to a gentle simmer. Allow it to cook for 20-25 minutes, stirring occasionally, so the flavors can meld beautifully.
Just before serving, fold in the fresh spinach (or kale) and cook for an additional 5 minutes until the greens are just wilted and vibrant.
Taste the soup and season with sea salt and freshly ground black pepper according to your preference.
Ladle the soup into bowls while hot, garnishing each serving with a sprinkle of fresh parsley and, if desired, a generous dusting of grated Parmesan cheese on top for a rich finish.