Line a loaf pan with parchment paper, leaving some overhang on the sides, and spray lightly with neutral cooking oil.
Pour the 2 cups of apple cider into a saucepan and bring to a boil over medium heat. Let the cider boil for about 45 minutes, stirring occasionally, until it reduces down to roughly 1/4 cup of thicker, darker syrup.
Add the butter chunks, heavy cream, granulated sugar, light brown sugar, vanilla bean paste, and apple pie spice into the pan with the reduced cider.
Stir everything together until combined and return the mixture to a boil.
Attach a candy thermometer to the side of the pan and cook the boiling caramel until the temperature reaches 250°F to 252°F tops.
Immediately remove the pan from the heat and pour the caramel into the prepared loaf pan.
Place the loaf pan into the refrigerator to chill and set for 10 minutes.
Remove the pan from the fridge and sprinkle the flaky salt evenly over the top surface.
Return the pan to the refrigerator to set for 2 to 3 hours (or allow it to set at room temperature for 4 to 5 hours).
Once fully set, lift the caramel slab out of the loaf pan using the parchment paper overhang. Lightly coat a sharp knife with neutral oil and cut the caramel into neat, bite-sized rectangles. Cut sheets of wax paper into rectangles, wrap each caramel tightly inside, and twist the ends to seal.
Store wrapped caramels in an airtight container at room temperature for about a week or in the refrigerator for a few weeks.
Allow chilled caramels to sit at room temperature before eating so they become soft and chew easily.