Line an 8-inch square pan with parchment paper, making sure to leave about 1" hanging over the edges for easy removal. Coat with a bit of vegetable oil and set aside.
Pour cider into a medium saucepan and boil on medium-high for about 20 minutes or until the cider is reduced to 1/3 c. Set aside to cool.
In a small bowl, combine 2/3 c. cream, cinnamon, nutmeg, allspice, and reduced apple cider, set aside.
In a large, heavy saucepan, combine the sugar, remaining 1/3 c. whipping cream and enough water to reach the 1/2 c. line on the measuring cup, and corn syrup. Cook over medium heat until the sugar dissolves. Insert the candy thermometer and simmer until the syrup reaches 234 degrees.
Remove from heat and slowly whisk in the cream mixture. Add the cubed butter and stir until the cream and butter are fully incorporated. Return the pan to heat and re-insert the candy thermometer. Cook over medium heat, stirring frequently, until the temperature reaches 248 degrees.
Remove from heat and pour the caramel into the prepared pan. Let the mixture cool completely at room temperature or in the refrigerator. Cut the caramels into 1/2" squares and wrap each caramel in wax paper. Store in an airtight container or in the refrigerator for up to 2 weeks.