Based on caldo verde—the Portuguese potato and kale classic—this soup gets a Cajun kick with the addition of andouille.
Heat oil in a large pot over medium heat. Sauté onions, carrots, celery, and a good pinch of salt until tender, about 6 minutes. Deglaze pot with white wine, then add potatoes, sausage, kale, thyme, garlic, and stock.
Bring to a boil, then reduce heat and let simmer until the potatoes have begun to break down, about 45 minutes. Adjust seasoning with salt and pepper and serve.