In a large saucepan over medium heat, cook onion and garlic in 3 tablespoons olive oil for 3 minutes. Stir in potatoes and cook, stirring constantly, 3 minutes more. Pour in water, bring to a boil, and let boil gently for 20 minutes, until potatoes are mushy.
Meanwhile, in a large skillet over medium-low heat, cook Chorizo sausage until it has released most of its fat, 10 minutes. Drain.
Mash potatoes or puree the potato mixture with a blender or food processor. Stir the sausage, salt and pepper into the soup and return to medium heat. Cover and simmer 5 minutes.
Just before serving, stir Collard Greens into soup and simmer, 5 minutes, until Collard Greens are tender and jade green. Stir in the remaining tablespoon of olive oil and serve at once