1. In a large pot, heat the oil over moderately low heat. Add the sausage and cook, turning, until browned, about 10 minutes. Remove the sausage from the pot and, when it is cool enough to handle, cut it into slices. Pour off all but 1 tablespoon fat from the pan.
2. Add the onion and cook, stirring occasionally, until it is translucent, about 5 minutes. Add the garlic to the pan and cook, stirring, for 1 minute longer.
3. Add the water, broth, and salt and bring the soup to a boil. Add the sausage, potatoes, and red-pepper flakes and bring back to a simmer. Cook, partially covered, for 2 minutes. Add the kale and bring the soup back to a simmer. Cook, partially covered, until the potatoes and kale are tender, about 6 minutes longer. Add the black pepper.
Menu Suggestions: An interesting bread completes this meal with aplomb. Try corn bread or tomato-topped Italian focaccia. A good crusty loaf of white bread will do fine, too.
Wine Recommendation: An aromatic, acidic white wine such as a sauvignon blanc is always a great choice for leafy greens. But the heartiness of this country soup can also work well with a full-bodied Portuguese red wine such as a Dão.