Add the apple cider and cinnamon to a small saucepan over medium-high heat. Let it cook for about 18 to 20 minutes, stirring occasionally, until it reduces down to roughly ¼ cup. Set this fragrant syrup aside while you work on the caramel base.
Spread the granulated sugar evenly across the bottom of a heavy-bottomed saucepan over medium-low heat. Resist the urge to stir at first — just let the sugar melt naturally around the edges before touching it at all.
Once a good amount of sugar has melted, gently stir with a wooden spoon so everything melts evenly. Keep cooking until the sugar turns a deep amber color, which usually takes another 5 to 10 minutes. Watch closely so it doesn't burn.
Lower the heat and carefully stir in the butter a little at a time until it's fully melted into the caramel. The mixture will bubble, so keep stirring steadily and don't walk away.
Slowly pour in the warmed heavy cream while whisking constantly. It will bubble up quite a bit here too, so pour gradually and keep your face away from the steam.
Stir in the reduced apple cider, vanilla extract, and a pinch of kosher salt. Mix until the sauce looks smooth and glossy, then let it cook on low for another 5 to 10 minutes.
Remove the pan from the heat and let the sauce sit. It will continue to thicken as it cools, so don't panic if it seems a little thin at first. Serve it warm or chilled, whichever you prefer.