Finely dice the onion and mince the garlic. Shred the kale or cabbage and set aside. If desired, you can use a combination of both kale and savoy cabbage. Thinly slice the sausage and set aside.
In a heavy-bottomed pot, heat the olive oil over medium-low heat. Add the onion and garlic, followed by a pinch of salt, and sweat for about 5 to 10 minutes or until translucent.
In the meantime, peel and dice the potatoes. Once the onions are translucent, add the potatoes, along with another pinch of salt, and cook for a few minutes to soften.
Increase the heat to medium-high and add the stock, along with another pinch of salt. Bring to a simmer. Cover and let simmer for approximately 10 minutes while you cook the sausage.
Heat a fry pan over medium heat and add the olive oil, followed by the sausage. Cook the sausage until the fat begins to render and the sausage just begins to brown. Remove with a slotted spoon and drain on paper towels.
*Note: Chouriço (spicy Portuguese chorizo), linguiça (smoked Portuguese sausages) or Kielbasa can be used to make this soup. For a vegetarian soup, simply omit the sausage.
Reserve the fat in the pan. This will likely have a nice deep red color from the sausage and can be used to add color to the soup once done.
Once the potatoes have cooked for about 10 minutes, mash them slightly with a potato masher. Add the kale and/or savoy cabbage and bring the soup up to a simmer for about 5 minutes until the kale is tender.
Mash the potatoes once again until you achieve the desired consistency. Stir in the sliced sausage and season to taste with salt and pepper.
Note: For extra color, stir in some of the reserved fat, if desired. Alternatively, you can mix a bit of Spanish paprika and a bit of olive oil together and add it to the soup.
Ladle into warmed bowls and drizzle with olive oil. Serve.