Combine the potatoes and salted water to cover in a medium saucepan. Bring to a boil and cook until the potatoes are fork tender, about 15 minutes. Drain and set aside.

Meanwhile, cook the bacon in a Dutch oven or soup pot over medium heat until browned and crispy. Remove the bacon to a paper towel lined plate with a slotted spoon, reserving the bacon grease in the Dutch oven.

Add the onion and garlic to the bacon drippings and cook until tender, about 5 minutes. Add the flour and stir until combined. Add the chicken broth, milk, and paprika and bring to a boil. Cook until the mixture is thickened.

If desired, use an immersion blender to puree the soup. (Or, puree the soup, in batches, in a blender until smooth. Return the soup to the pot.)

Add the potatoes to the Dutch oven. Use a potato masher to mash the potatoes into smaller pieces. Return the soup to a simmer. Set aside some of the shredded cheese and bacon for garnish. Stir the remaining cheese and bacon into the soup and stir until the cheese melts. Season with salt and pepper to taste.

To serve, divide the soup evenly between serving bowls. Top with shredded cheese, bacon, sour cream, and chives.