Pour the apple cider in a medium saucepan and simmer over moderate heat, stirring occasionally, until reduced to 1/2 to 2/3 cup, about 1 hour.
Butter the bottoms and sides (get into the corners, too!) of a 9X9-inch square baking pan. (Alternately, you can line with parchment and butter the parchment – this may make it easier to pull the slab of caramels out of the pan after they have cooled in order to cut and wrap them.) Set aside.
Heat the cream in a saucepan or in the microwave until steaming. Keep warm.
For the caramels, in a large, heavy-bottomed pot (at least 5- or 6-quarts), stir together the sugar, corn syrup, and water, taking care to not splash the mixture up the sides of the pot. Clip a candy thermometer onto the side of the pan.
Bring the mixture to a boil over medium heat WITHOUT STIRRING or moving the pan. As it begins to boil, fill a cup with water and use a pastry brush to wash down the sides of the pan so there are no granules of sugar sticking to the sides of the pan (you probably won’t need to repeat this after the sides have been well-cleaned). This prevents the caramel mixture from crystallizing in later steps.
Cook until the boiling sugar turns a light-to-medium amber color and registers 325 to 345 degrees F on the thermometer, about 15-20 minutes .
Slowly and carefully pour the warm cream into the caramel. Add the reduced apple cider, butter and salt. The mixture will bubble high during this step but will go down after a few minutes.
Begin stirring the caramel with a heatproof silicone spatula with a flat top (a flat edge does better at preventing the caramel from burning than a rounded edge). Avoiding scraping the edges of the pan, and continue to cook, stirring constantly and slowly, until the mixture reaches 245 to 248 degrees F, about 10-15 minutes (these caramels tend to be softer than a *normal* caramel, likely due to the apple cider, so if you want a firmer caramel, consider adding 2 to 3 degrees to the cooking temperature).
Off the heat, stir in the vanilla and cinnamon.
Immediately pour the caramel mixture into the prepared pan.
Let the caramels cool completely. Lift the caramels from the pan and transfer to a cutting board (I use a large, metal spatula to gently peel the whole slab of caramel out of the pan).
Cut into squares using a sharp knife or bench scraper, wrap, and store in an airtight container at cool room temperature for up to two weeks.
Notes
Apple Cider: the best kind of apple cider to use for these caramels is the "fresh" apple cider common in the fall months. Look for apple cider that is unfiltered (it will be cloudy, not clear like apple juice) with no added sugar. The apple cider can be boiled down several days in advance. Refrigerate until ready to use. Before making the caramels, heat the reduced apple cider until warm and pourable (if it is added to the boiling sugar cold from the refrigerator, it can cause the caramel to crystallize or seize). Double Batch: this recipe can be doubled (for a 9X13-inch pan of caramels). Use a larger pan so it doesn’t boil over. A double batch will take longer to come to temperature at each step.Time: the exact time for each step will depend on how low or high you moderate the heat – as well as if you have a gas or electric stove.Elevation:I live at 2,400 feet elevation which is where this recipe has been tested. If you live at higher or lower elevation, you may need to adjust the final cooking temperature 2 degrees for every 1,000 feet elevation difference (subtracting for higher elevation and adding for lower elevation). For instance, if you live at sea level, you may need to add 4 degrees to the final cooking temperature. If you live at 5,000 feet elevation, you may need subtract 4 to 5 degrees from the final cooking temperature. A lot depends on the desired firmness/chewiness of the caramels, so there is some leeway in the exact number of degrees for cooking the caramel. In my experience, a difference of 2 to 4 degrees won't make or break a caramel recipe, so don't stress too much about this. Just keep track of the outcome and make adjustments in subsequent batches as needed. Several people have commented that these apple cider caramels turn out softer than "normal" caramels (likely due to the apple cider). Given that, I suggest adding a few degrees to the cooking temperature if you want a firmer caramel.