In a large pot, bring the 4 cups of cider to a boil, and cook on medium-high heat for 35-45 minutes, stirring once in a while, until it is reduced to a dark, thick syrup, between 1/3 and 1/2 cup in volume.
Meanwhile, set out your other ingredients, because time is of the essence when the candy begins cooking. Line the bottom and sides of an 8- inch square metal baking pan with 2 long sheets of perpendicular parchment. Set it aside. Stir the cinnamon and 1 tsp of the flaky salt together in a small dish.
Once you are finished reducing the apple cider, stir in the butter, sugars, and cream. Return the pot to medium-high heat, and let it boil until the thermometer reads 252 degrees (about 5 minutes).
Immediately remove caramel from heat, add the cinnamon-salt mixture, stir to distribute it evenly.
Pour caramel into the prepared pan. Sprinkle with the remaining 1 tsp of flaked salt.
Allow to cool until it's firm -- about 2 hours. Once caramel is firm, transfer it to a cutting board. Use a well-oiled knife, oiling it after each cut (Deb's invaluable advice on this), to cut the caramel into 1x1-inch squares. Wrap each one in a 4-inch square of waxed paper, twisting the sides to close. Caramels will be somewhat on the soft side at room temperature, and chewy/firm from the fridge.