In a large soup pan heat 3 tablespoons olive oil over medium low heat and sauté the onion until soft, about 8 minutes. Add the garlic and cook for an additional minute, stirring.
Add the potatoes and water to the pot. Bring to a boil, cover and simmer for fifteen minutes or until potatoes are fork tender. Remove from heat and set aside to cool.
In a medium sauté pan over medium heat, add one tablespoon olive oil and sauté the sausage. Sauté, turning frequently to brown all sides. Transfer to a plate lined with paper towels to drain.
If you like a thick soup, take some of the potatoes and either mash with a fork or put in a blender and puree. Add back to the pot. If you do not want thick soup, skip this step. Next, add the sausage to the pot and simmer gently for five minutes.
In the meantime, trim the thick stems from the collard green leaves and then cut into a fine chiffonade. Add the greens to the soup and simmer gently for another five minutes. If the greens are prepared ahead of time, add them fully cooked and simmer a few minutes.
Season to taste with salt and pepper. Ladle the soup into the bowls. Drizzle with a little olive oil, if desired. Serve hot.