Place half of the beans in a blender or food processor and mix until creamy. As an alternative you can also use an immersion blender or mash them with a fork.
In a large pot, heat 1 tablespoon of olive oil over medium heat. Add sliced onion and minced garlic, then sauté for 2 - 3 minutes. If necessary, add a tablespoon of water to prevent sticking.
Add to the pot diced carrot, diced celery and tomato paste, then allow to wilt for about 5 minutes.
Add blended beans, kale and vegetable broth. Give it a stir and bring to a boil, then lower the heat and let simmer, covered, for about 5 minutes. Stir frequently.
Stir in the remaining beans, salt and pepper to taste. Simmer for additional 5 minutes, then add 1 tablespoon of olive oil. Taste and adjust with more seasonings, if necessary.
Serve warm, with sourdough bread and a drizzle of olive oil.