How to Make It
Preheat the oven to 400°. In a large saucepan, heat the 2 tablespoons of olive oil. Add the onion, garlic and a generous pinch of salt and cook over moderate heat, stirring occasionally, until just starting to soften, about 5 minutes. Add the water and potatoes and bring to a boil. Cover and simmer over moderately low heat, stirring occasionally, until the potatoes are very tender, about 25 minutes.
Meanwhile, on a rimmed baking sheet, roast the sausages for about 20 minutes, until an instant-read thermometer inserted in each one registers 165°. Transfer to a carving board and let rest for 5 minutes, then slice crosswise 1/2 inch thick.
Working in batches, puree the soup in a blender until very smooth. Return the soup to the saucepan and bring just to a simmer over moderate heat. Add the kale and simmer until softened, about 3 minutes. Stir in the vinegar and sugar, then season with salt. Ladle the soup into bowls, top with the sliced chorizo and a drizzle of olive oil and serve.