In a stockpot, warm the olive oil over medium heat. In the hot oil, cook and sauté the onion for 5 to 10 minutes, or until transparent. Add the garlic and stir while cooking for two minutes or until fragrant.

Cook chorizo and ham with onion mixture for 3 to 4 minutes, stirring occasionally, until gently browned. Add chicken stock after combining the potatoes and turnips with the chorizo mixture. When the potatoes and turnips are cooked, about 20 minutes after bringing the stock to a boil, turn the heat down to medium-low, cover the stockpot, and simmer.

Cannellini beans and turnip greens are added to the soup, and the heat is raised to medium. Cook for at least 3 minutes, or until the greens are the desired softness.