In a small saucepan, combine the brown sugar, granulated sugar, and cinnamon sticks. Bring the mixture up to a boil over high heat, reduce the heat to low, and allow it to simmer for 10 minutes.
Pour the apple cider and two tablespoons of cinnamon syrup into a microwave-safe mug, microwave for 1-2 minutes until it's warmed.
Top with whipped cream and drizzle the caramel over the top.