Pour apple cider into a small sized saucepan. Cook over medium heat and bring the apple cider to a simmer.
Continue simmering until the apple cider reduces to 1/3 cup, about 30 to 40 minutes.
In the meantime, butter the sides of an 8 x 8 inch dish and cover the bottom with parchment paper for easy removal of caramels. Set aside.
In a small bowl, combine 2/3 cup heavy cream, cinnamon, nutmeg, allspice, salt and the reduced apple cider. Set aside.
In a glass measuring cup, add 1/3 cup heavy cream. Then add enough water to get the liquid to the 1/2 cup line on the measuring cup. Pour contents into a large pan.
Add sugar and corn syrup. Stir together to combine.
Heat over low until the sugar dissolves, stirring frequently.
Then, insert a candy thermometer and simmer, stirring frequently, until the syrup boils, about 25 minutes.
Continue cooking, without stirring, until the syrup reaches 234F.
Remove from heat and slowly whisk in the cream and spice mixture.
Add butter and stir until combined.
Return pan to heat and cook over low, while stirring, until the mixture boils.
Then stop stirring and continue cooking until it reaches 250F.
Pour caramel into your 8 x 8 inch dish. Let mixture cool slightly before adding sea salt. Cool in the refrigerator until it is set.
When it is set, remove caramel from pan by lifting the parchment paper. Place on a cutting board and cut caramel into 3/4 inch squares.
Wrap each caramel in a small piece of wax paper by twisting the ends around the caramel.
Store in an airtight container in the refrigerator for up to 2 weeks. Makes about 80 caramels.