Heat olive oil in a large pot over medium heat. Saute onions, celery, and carrots until softened. Add garlic, paprika, rosemary, salt, and pepper. Cook for another minute.
Pour in vegetable broth, liquid smoke, and 2 cans of beans. Bring to a boil, then reduce heat and simmer for 15-20 minutes until vegetables are tender. Remove from heat and puree the soup with an immersion blender until slightly chunky.
Return the mixture to the pot over medium-low heat. Add the remaining can of beans and stir until heated through. Season with additional rosemary, salt, and pepper to taste.