Heat 1 tablespoon olive oil in a Dutch oven or stock pot over medium-high heat. Add the onions, carrot, celery, and 1 teaspoon salt. Cook, stirring occasionally, until the vegetables are soft, about 5 minutes. Add the garlic, thyme, red chili flakes, and ½ teaspoon black pepper. Cook, stirring, for 30 seconds. Add the broth and beans and bring to a boil.
Once the soup has boiled, put half the soup in a blender with the vinegar and blend until smooth. Return to the pot with the rest of the soup and add the kale. Bring to a boil again, then reduce the heat and let simmer until the kale is wilted. Taste and add more salt and pepper, if desired.
Serve with extra olive oil to drizzle on top and hot sauce.