Prepare the Caramel Sauce
In a medium heavy-bottomed saucepan, spread sugar in an even layer over medium heat. As the sugar begins to melt, gently swirl the pan – avoid stirring as this can cause crystallization.
Once the sugar has completely melted and reached a deep amber color (around 350°F if using a candy thermometer), carefully add the butter pieces while whisking vigorously. The mixture will bubble intensely.
Continue whisking until butter is fully incorporated, then slowly pour in the heavy cream while continuing to whisk. Allow the mixture to boil for exactly 1 minute, then remove from heat and stir in the sea salt.
Transfer to a heat-safe container and set aside to cool slightly.
Warm the Apple Cider Base
Pour the apple cider into a large pot over medium heat. Add the cinnamon sticks, cloves, star anise, orange slices, and apple wedges.
Bring the mixture to a gentle simmer (never a rolling boil), then reduce heat to low and cover partially.
Allow the mixture to simmer for 15-20 minutes, stirring occasionally to ensure the spices infuse evenly throughout the cider.
Combine and Finish
Remove the spiced cider from heat and strain out all the solid ingredients using a fine-mesh strainer. Return the filtered cider to the pot over low heat.
Add ¾ cup of your prepared caramel sauce to the warm cider, whisking gently until completely incorporated. Reserve the remaining caramel for garnishing.
Heat the combined mixture for an additional 2-3 minutes to ensure everything is well-blended and has reached your desired serving temperature.
Serve
Pour into mugs and garnish as desired with whipped cream, a drizzle of reserved caramel sauce, cinnamon sticks, apple slices, or marshmallows.
For an extra special presentation, rim the mugs with cinnamon sugar before pouring in the cider.