Pour the apple cider into your saucepan and add the pumpkin puree along with the brown sugar. Whisk everything together over medium heat until the pumpkin is fully incorporated and there are no lumps left. This only takes a minute or two of steady whisking.
Stir in the cinnamon, nutmeg, and cloves once the pumpkin has dissolved into the cider. Let the mixture continue heating gently, whisking occasionally so nothing settles or scorches on the bottom of the pan.
Bring the mixture to a gentle simmer and let it cook for about 10 to 15 minutes. This step lets all those warm spices really infuse into the cider, so don't rush it even if you're tempted to serve it early.
While the cider simmers, add your heavy cream, powdered sugar, and the extra cinnamon to a mixing bowl. Beat with a hand mixer until soft peaks form, which usually takes two to three minutes on medium-high speed.
If you want to turn this into a cocktail, stir your bourbon, brandy, or apple liqueur directly into the saucepan during the last few minutes of simmering. Skip this step entirely if you're keeping things family-friendly.
Ladle the hot cider into mugs and top each one generously with the cinnamon whipped cream. Finish with a light dusting of extra cinnamon-sugar, an apple slice, and a cinnamon stick for that finishing touch.