Heat olive oil in a large soup pot over medium high heat
Add the onion and garlic. Cook, stirring occasionally for 4 to 5 minutes until onion is softened.
Add the sausage and cook, stirring occasionally, until lightly browned (kielbasa) or fully cooked (Italian sausage)
Add the broth, water and tomato and bring to a boil; immediately reduce heat to simmer.
Add beans and about 1/2 of the greens, allowing them to wilt slightly before adding remaining greens.
Cook until the greens are completely wilted and the broth is flavorful, about 5 more minutes for wilted but still crisp greens. (I prefer fully cooked greens so cook for ~15 min or more)