Heat a large saucepan coated with cooking spray over medium-high heat. Add carrots, onion, garlic, and kielbasa; sauté 3 minutes, stirring occasionally. Reduce heat to medium; cook 5 minutes. Add the broth, Italian seasoning, pepper, and beans. Bring to a boil, reduce heat, and simmer 5 minutes.
Place 2 cups of the soup in a food processor or blender, and process until smooth. Return the pureed mixture to pan. Simmer an additional 5 minutes. Remove soup from heat. Add the spinach, stirring until spinach wilts.