In a stockpot, heat the olive oil over medium heat. Add the onions and garlic and cook until soft and translucent.
In a frying pan, cook the sausage, slice it and set aside for later.
Add the potatoes to the stockpot and cover with water. Bring to a boil and lower the heat, simmering until the potatoes are almost done, about 15 minutes.
Remove the pot from the heat and crush some of the potatoes using a potato masher or wooden spoon to thicken the broth. Return the pot to the heat and bring to a boil. Add the greens and simmer for 15-20 minutes.
Season with salt and pepper, ladle into bowls, and garnish with sausage.