Combine the vinegar, water, sugar, salt, and star anise in a small saucepan over high heat, stirring until the sugar and salt are dissolved. Bring to a boil. Place the apples in a small bowl. Once the liquid comes to a boil, pour over the apples. Let sit at room temperature for 1 hour. Drain the apple slices and pat dry with paper towels.
Meanwhile, place a large skillet over medium-high heat. Add the bacon and cook for about 6 minutes, until golden and crispy on both sides. Drain on paper towels.
Preheat a panini press. Place 4 bread slices on a clean work surface. Divide the cheddar cheese, bacon, and pickled apples between the bread slices and top the sandwiches with the remaining bread slices. Grill the sandwiches for 4 to 5 minutes, until the bread is golden brown and the cheese is melted. Transfer the sandwiches to a cutting board. Cut each sandwich in half and serve.