In a large pot over medium heat, cook the bacon until it reaches a crisp texture, roughly 4 to 5 minutes per side. Remove the bacon and place it on a paper towel-lined plate to drain excess fat, allowing it to cool slightly before chopping into rough pieces. Reserve approximately 2 tablespoons of the rendered bacon fat in the pot.

Raise the heat to medium-high and add the onion, apples, and potato to the pot. Sauté while stirring frequently until the apples become tender, approximately 8 minutes. Add the chicken broth, apple juice, ¾ teaspoon salt, and freshly ground black pepper to taste. Bring the mixture to a gentle simmer and cook until the potato is fully tender, about 10 to 12 minutes. Gradually incorporate all but 2 tablespoons of the cheddar cheese, stirring until melted. Working in batches, carefully transfer the hot soup to a blender and puree until smooth. Return the puréed soup to the pot and adjust seasoning with additional salt and pepper as needed.

Preheat the broiler. Spread the toasted rye bread with Dijon mustard, then sprinkle with the reserved 2 tablespoons of cheddar cheese. Broil briefly, about 30 seconds, until the cheese melts. Cut the bread into 1-inch squares to serve as cheese croutons.

Serve the soup in bowls, garnished with the chopped bacon, fresh chives, cheese croutons, and additional freshly ground black pepper as desired.