Heat oil in a large soup pot. Add the onion and cook, stirring often, until the onions starts to soften. Add the carrots, celery, and leeks. Continue cooking, stirring often, for about 5 minutes. Add the garlic and cook for another 30 seconds, being careful not to let it burn.
Next add the tomato paste and stir well. Let cook for 30 seconds then add beans, diced tomatoes, broth, thyme, and butternut squash. Add salt and fresh ground black pepper, to taste. (It might not need much salt if the broth is salted.) Bring to a simmer and let cook for about 15-20 minutes, or until the squash is tender.
Add the chopped kale and let cook for another 5-10 minutes. Taste and add more salt and pepper, if needed.
Ladle into bowls and serve hot with warm rolls or bread on the side.