In a medium saucepan, bring the apple cider to a boil over medium high heat. Continue boiling, stirring occasionally, for 10-15 minutes until the cider reduces to a dark, thick syrup that is about 1/4 cup in volume. Watch very carefully in the last few minutes to ensure the cider doesn’t burn.
Reduce the heat to medium-low, then add the granulated sugar and brown sugar. Let bubble for 2 minutes, until the sugar dissolves, then add the butter and heavy cream.
Boil over medium-low, whisking constantly, until the mixture thickens somewhat, 3-5 minutes. The caramel will still seem fairly thin at this point.
Remove from the heat completely and stir in the vanilla, cinnamon, and salt. Allow the caramel to cool for 5 to 10 minutes, until it reaches a thicker but still pourable consistency (it will still be warm) or let it rest for longer to cool to a more solid, dip-like texture. To serve, drizzle over ice cream, pie, apple slices, coffee, or just eat with a spoon.
Notes
TO STORE: Leftover caramel sauce will keep in an airtight container in the refrigerator for up to 1 week.
TO REHEAT: Microwave on high in a microwave-safe container until just warm (about 10 or so seconds depending upon your microwave), then stir until smooth.
TO FREEZE: Apple cider caramel sauce may be frozen in an airtight container for up to 3 months. Defrost in the fridge overnight, then reheat as directed above.