Heat olive oil in a large pot over medium heat. Add the diced onion, carrots, and celery. Cook for 8-10 minutes, stirring occasionally, until the vegetables are softened and the onion is translucent.

Stir in the minced garlic and cook for 1 minute until fragrant. Add the rosemary sprigs and bay leaves to the pot.

Pour in the drained white beans and vegetable broth. Stir everything together and bring the soup to a boil over high heat.

Once boiling, reduce the heat to low and let the soup simmer uncovered for 30 minutes, allowing the flavors to meld together.

Remove the rosemary sprigs and bay leaves. Use an immersion blender to partially blend the soup, leaving some beans whole for texture. Alternatively, transfer 2 cups of soup to a blender, puree, and return to the pot.

Taste the soup and season with salt and pepper as needed. If the soup is too thick, add more broth or water to reach your desired consistency.

Ladle the soup into bowls and serve hot. Garnish with a drizzle of olive oil, fresh herbs, or grated Parmesan cheese if desired.