Heat oil in a stockpot over medium heat. Add onion and sauté until translucent, 5 to 10 minutes. Add garlic; cook and stir until fragrant, 1 to 2 minutes.
Stir in chorizo and ham; cook and stir until lightly browned, 3 to 4 minutes. Add potatoes and turnips, then pour in stock and bring to a boil. Reduce the heat to medium-low, cover, and simmer until potatoes and turnips are tender, about 20 minutes.
Increase the heat to medium and stir in beans and greens; cook until greens are tender, at least 3 minutes.
