How to Make It
In a large saucepan, cook the bacon over moderate heat until crisp. Remove the bacon with a slotted spoon and drain on paper towels. Pour off all but 2 tablespoons of the bacon fat or, if you don't have 2 tablespoons, add enough cooking oil to make up the amount. Reduce the heat to moderately low.
Add the onion and cook, stirring occasionally, until translucent, about 5 minutes. Stir in the potatoes, water, and salt and bring to a boil. Reduce the heat and simmer, covered, stirring occasionally, until the potatoes are tender, 15 to 20 minutes.
Remove half the soup from the pan and puree in a food processor. Alternatively, mash some of the potatoes with a potato masher. Return the puree to the pan. Over low heat, add the cheese and stir until melted. Remove the pan from the heat. Taste the soup and add more salt if needed. Serve the soup topped with the bacon and chives.
Boiling potatoes have less starch than baking, or Idaho, potatoes and consequentially hold together better when boiled. This is why they're often used in soups and for potato salads. Not in this soup, though. Since we want some of the potato to break down into smaller pieces and thicken the soup, baking potatoes are the perfect choice.