To make the caramel sauce, warm the cream in a small saucepan over low heat. (You’ll want to slightly warm up the cream to prevent curdling when it is added to the hot liquid).
Add the sugar and water to a heavy-bottomed saucepan and stir to combine. Set the spoon aside and do not stir the sugar mixture again.
Bring mixture to a boil over medium-high heat. If sugar crystals remain on the sides of the pan, gently brush them back down with a moistened silicon baking brush.
Continue boiling until the mixture turns a nice amber color. Do not overcook. If the mixture gets too dark at this stage, you will need to start over. If a dark spot forms on one side due to uneven heating, lift the pan and gently swirl until the color is even again. Return pan to the burner and reduce heat when the desired color is achieved.
Slowly whisk in the warmed cream until thoroughly incorporated. Be very careful while doing so because the sugar mixture will be extremely hot and will bubble up when the cooler cream is added.
Remove from heat and add butter. Stir with a clean spoon until butter is totally incorporated into the mixture.
Cool and store in an airtight container in the refrigerator for up to 5 days.
To make the maple whipped cream, blend 1 pint of heavy whipping cream with a hand or immersion blender until it doubles in size and changes texture. Then, drizzle maple syrup into the bowl and continue blending until the mixture is light and fluffy.
To make the apple cider, add the apple cider, brown sugar, pumpkin pie spice, vanilla, and cinnamon sticks to a slow cooker. Cover and cook on low for 3 hours.
After 2½ hours, stir in ½ cup caramel sauce. Cover and allow the flavors to mingle for the remaining 30 minutes.
Remove the cinnamon sticks and discard.
To serve, ladle the hot cider into mugs and top with maple whipped cream and drizzle with additional caramel sauce.