In a large pot or Dutch oven, combine the potatoes, onion, garlic, broth, and water. Bring to a boil over high heat, then reduce the heat to low and simmer until the potatoes are tender, 15-20 minutes.
In a separate saucepan, melt the butter over medium heat. Add the flour and cook, stirring constantly, for 1-2 minutes. Slowly whisk in the milk and cream, and continue cooking until the mixture thickens, 5-7 minutes.
Stir the milk mixture into the soup, along with the cheddar cheese, bacon, and chives. Cook until the cheese is melted and the soup is hot, 5-7 minutes.
Season the soup with salt and pepper to taste. Serve hot, garnished with additional cheese, bacon, and chives, if desired. Enjoy!