Heat the oil in a Dutch oven or large heavy bottomed saucepan over medium-high heat. Add the onion and cook for 3 minutes. Add the broth and the potatoes. Bring to a simmer. Cook the potatoes, covered, until they are fork tender, about 15 minutes.

Combine the flour and the milk in a large measuring cup. Bring to a boil, stirring often, being careful to not let the milk boil over. Cook for 1 minute. Coarsely mash potatoes into soup using a potato masher. For a smoother texture, use an immersion blender to blend the soup. Remove from heat and stir in sour cream, salt, and pepper.

Ladle the soup into four bowls and top with the bacon, cheese, and green onions.