Heat the oil in a medium-large soup pot over medium heat. Add the onions, carrots, and celery to the pot and stir. Sauté the vegetables until lightly softened and translucent, about 5 minutes.
To the pot, add the garlic, chili flakes, and rosemary. Stir and cook until garlic is fragrant, about 30 seconds. Add the navy beans to the pot and stir. Add the vegetable stock to the pot and stir once more. Bring the soup to a boil.
Once boiling, ladle half of the soup into an upright blender. Add the lemon juice to the blender as well. Carefully bring the speed of the blender up to high and blend until this portion of the soup is totally liquified. Pour this liquified portion back into the pot. Season the soup with salt and pepper.
Add the kale to the pot and bring the soup to a boil. Once the kale is slightly wilted and bright green, season the soup once more with salt and pepper, if you find it necessary. Stir in the chopped parsley as well. Serve the soup hot.