In a large pot, cook the bacon over medium heat until it reaches a crispy texture, approximately 4 to 5 minutes per side. Once cooked, transfer the bacon to a plate lined with paper towels to drain excess fat and cool slightly before roughly chopping. Retain about 2 tablespoons of the rendered drippings in the pot.

Increase the heat to medium-high and add the chopped onion, diced apples, and potato to the pot. Cook while stirring frequently until the apples soften, which should take about 8 minutes. Incorporate the chicken broth, apple juice, 3/4 teaspoon of salt, and freshly ground pepper to taste. Allow the mixture to come to a simmer and cook until the potato is tender, approximately 10 to 12 minutes. Gradually stir in all but 2 tablespoons of the cheddar cheese until fully melted. Working in batches, carefully transfer the soup to a blender and puree until smooth. Return the blended soup to the pot and adjust the seasoning with additional salt and pepper as needed.

Meanwhile, preheat the broiler. Spread the toasted rye bread with Dijon mustard and sprinkle the reserved 2 tablespoons of cheese on top. Broil the bread until the cheese melts, which should take about 30 seconds. Once melted, cut the bread into 1-inch squares. Serve the soup in bowls, garnished with the chopped bacon, fresh chives, cheese croutons, and additional pepper to taste.