SYRUP: Pour one quart sweet apple cider into a cast iron saute pan over medium heat. Reduce the cider slowly to one cup. Remove from heat and let cool. It will have the consistency of thick syrup.
VINAIGRETTE: Whisk the apple cider vinegar and the apple syrup in a mixing bowl. Add the olive oil and salt and pepper to taste, mix together.
SALAD: Peel and slice the apples, then place the slices on a plate in a circular pattern. Toss the arugula with the vinaigrette. Place the salad on top of the apple slices. Put the goat cheese on top of the salad and serve.