Heat olive oil in a large soup pot over medium heat. Add the diced onion, carrot, and celery, then cook for 5 minutes until softened.

Add the minced garlic and cook for 30 seconds until fragrant.

Mix in the drained beans, cubed potatoes, tomato paste, rosemary sprig, and paprika. Cook for 1 minute while stirring.

Add the dry white wine and scrape the bottom of the pot to loosen any browned bits, then simmer for 1 minute.

Pour in the vegetable broth and add the frozen spinach, salt, and black pepper. Bring the soup to a gentle boil, then lower the heat and simmer uncovered for 15 minutes until the potatoes are fork-tender.

Remove the rosemary sprig, then press some of the beans and potatoes against the side of the pot to thicken the soup while keeping some pieces whole.

Spoon the white bean soup into bowls and top with Parmesan cheese, olive oil drizzle, and fresh cracked pepper.

Serve immediately with crusty bread.