Boil the apple cider in a 4-quart saucepan over high heat, stirring occasionally, until reduced to a dark, thick syrup, between 1/3-cup and 1/2-cup (approximately 35 to 40 minutes).
Meanwhile, line the bottom and sides of an 8-inch square baking dish with parchment paper, leaving excess hanging over the sides.
In a small bowl, combine the cinnamon and salt, set aside.
After the cider has reduced, remove it from the heat and stir in the butter, sugars, and heavy cream. Return the pan to medium-high heat and attach a candy thermometer to the side. Let the mixture boil until the thermometer reaches 252 degrees F, about 5 minutes.
Immediately remove the caramel from the heat, add the cinnamon and salt, and stir several times with a wooden spoon. Pour the caramel into the prepared pan. Let sit until cool and firm, about 2 hours.
Once the caramel is firm, use the parchment overhangs to lift it out of the pan and transfer to a cutting board. Using a very sharp knife coated with non-stick cooking stray, cut the caramel into 1-inch squares. You may need to respray the knife several times during cutting to ensure clean slices.
Wrap each caramel in a 4-inch square of waxed paper, twisting the sides to close. The caramels can be stored in an airtight container for up to 2 weeks.