Cook the bacon in a large pot over medium heat until crisp, 4 to 5 minutes per side. Transfer to paper towels to drain; let cool slightly, then roughly chop. Pour out all but 2 tablespoons of the drippings from the pot.
Increase the heat under the pot to medium high. Add the onion, apples and potato and cook, stirring frequently, until the apples are soft, about 8 minutes. Add the chicken broth, apple juice, 3/4 teaspoon salt, and pepper to taste. Bring to a simmer and cook until the potato is soft, 10 to 12 minutes. Stir in all but 2 tablespoons of the cheddar until melted. Working in batches, transfer the soup to a blender and puree. Return to the pot and season with salt and pepper.
Meanwhile, preheat the broiler. Spread the bread with the mustard and sprinkle with the reserved 2 tablespoons cheese. Broil until the cheese melts, about 30 seconds, then cut into 1-inch squares. Ladle the soup into bowls and top with the bacon, chives, cheese croutons and more pepper.
If the bacon doesn’t render enough fat, use a little neutral oil or butter to make up the difference.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
Courtesy of Food Network Magazine, Photograph by Christopher Testani