Heat the apple cider in a nonreactive saucepan.
In a bowl, combine the softened butter, brown sugar, nutmeg, cinnamon, and cloves. Whip until the butter becomes creamy and the ingredients are incorporated. Place the graham crackers and pumpkin pie spice in a plastic baggie and crush with a rolling pin. Combine the rum extract with the non-dairy whipped topping. In a footed coffee glass, place a single cinnamon stick and a slice of spiced butter. Pour 1 shot whiskey into the glass. Ladle the hot cider to fill the glass. Garnish with a dollop of rum-flavored topping and a sprinkle of graham cracker crumb mixture. Serve warm.