Pour the apple cider into a small saucepan and bring it to a boil over medium-high heat. Let it boil steadily, stirring occasionally, for about 8 to 10 minutes until it reduces down to roughly 1/4 cup. It will look syrupy and darker in color. Pull it off the heat and set it aside. Have your warm heavy cream, butter pieces, and reduced cider all within arm's reach before you start the caramel, because once the sugar gets going you will not want to step away.

In your light-colored heavy-bottomed saucepan, combine the granulated sugar and water over medium heat. Stir gently just until the sugar dissolves, then stop stirring entirely. Swirl the pan gently if needed but do not use a spoon from this point forward, as stirring can cause the sugar to crystallize.

Let the mixture cook undisturbed for 8 to 12 minutes. Watch it closely. It will bubble vigorously, then start to turn pale gold around the edges. Once you see amber color beginning to develop at the edges, swirl the pan to even it out. You are looking for a deep amber color, like an old penny. This happens fast toward the end, so stay at the stove.

The moment the caramel reaches a deep amber and smells nutty and slightly smoky, pour in the warm heavy cream carefully. It will bubble up aggressively, this is normal. Stir with your spatula. Then pour in the reduced apple cider and stir again. Add the butter pieces and stir until fully melted and the sauce looks smooth and glossy.

Stir in the salt and vanilla. Taste carefully, it will be very hot, and adjust salt if needed. The sauce will look thin at this point but will thicken as it cools.

Pour the caramel into a heat-safe glass jar or measuring cup. Let it cool for 15 minutes before using, or cool completely and refrigerate. It will keep for up to 2 weeks covered in the refrigerator. Reheat gently before serving.