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.