The dark green cabbage traditionally used in this Gallecian "green" soup is not widely available beyond Spain's borders, and Cubans love this traditional soup. Kale or collard greens make a good substitute. A crusty bread often accompanies the soup, although a good American corn bread or other crusty bread is also nice for sopping up any bits remaining in the bowl. Don't forget the final flourish of olive oil. It will perfume the soup.
Bring a saucepan three-fourths full of water to a boil over high heat. Prick the sausages with a fork and add to the boiling water. Boil for about 5 minutes. Using tongs, transfer the sausages to a cutting board and, when cool enough to handle, slice them. (You may discard the sausage-flavored water or reserve it for making the soup.)
Rinse and drain the greens, then remove any tough stems. Working in batches, stack the leaves, roll up the stack like a cigar, and cut crosswise into very, very thin strips. Set aside
In a large soup pot over medium heat, warm the olive oil. Add the onions and sauté, stirring occasionally, until tender and translucent, about 10 minutes. Increase the heat to medium-high, add the potatoes and garlic and sauté, stirring often, until slightly softened, about 5 minutes. Add the water and 2 tsp. salt, reduce the heat to low, cover and simmer until the potatoes are very soft, about 20 minutes.
Scoop out about 2 cups of the potatoes and mash well with a potato masher or fork. Return them to the pan, add the sliced sausages and simmer until the sausages are cooked through, about 5 minutes more. Add the greens, stir well and simmer, uncovered, stirring occasionally, for 3 to 5 minutes. Do not overcook; the greens should be bright green and slightly crunchy. Season with salt and pepper.
To serve, ladle the soup into warmed bowls and drizzle each serving evenly with extra-virgin olive oil. Fresh bread to accompany this delicious soup.