In a 2-quart pot, warm the oil or butter over medium heat. Add the chopped onions and cook, stirring frequently, until the onions are soft and lightly golden, 5 to 7 minutes.
Transfer the onions to a food processor or blender. Add the drained potatoes and the stock. Process until smooth, then add the cream, salt, and pepper and process again to combine.
Return the purée to the soup pot and cook over medium heat until hot throughout, 2 to 3 minutes.
Season to taste with more salt and pepper as desired. Serve warm, topped with parsley, parmesan, or other garnish of your choice.
