Heat the olive oil in a large pot over medium heat. Add the onion, garlic, and carrots, then cook for 5 minutes until the vegetables soften.
Stir in the diced tomatoes with their juices and cook for 2 minutes.
Pour in the vegetable broth, then add the cannellini beans, rosemary, salt, and black pepper. Bring the mixture to a simmer.
Add the chopped kale and cook for 8 to 10 minutes until the kale wilts and the soup thickens slightly.
Taste and adjust seasoning if needed before serving.