Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion and sauté until it begins to soften and turn golden.
Stir in the garlic, carrots, and celery. Cook for about 10 minutes, stirring occasionally, until the vegetables soften and develop some browning.
Pour in the white wine and let it cook for about 5 minutes, until most of the liquid has evaporated.
Add the cannellini beans, tomato paste, 2 1/2 cups broth, salt, pepper, red pepper flakes, Italian seasoning, bay leaves, thyme, and oregano, and stir to combine. Stir well to combine.
Let the soup come to a boil, then lower the heat, cover the pot, and simmer for 15 minutes.
Remove and discard the bay leaves. Scoop out about 2 1/2 to 3 cups of the soup, place it in a blender, and blend until smooth. Pour the blended soup back into the pot and stir it in well. Add extra broth if you like the soup a bit thinner.
Stir in the chopped kale and simmer for a few minutes until it wilts. Taste and adjust seasoning with more salt, pepper, or a squeeze of lemon juice.
Serve hot with crusty bread for dipping.