In a saucepan, heat the cider.
Pour the cider into a mug, and top with the rum and liqueur.
Garnish with 2 cinnamon sticks.
*Pie spice liqueur: In a small skillet, toast 1 tsp whole cloves, 1 tsp whole allspice berries, 3/4 tsp white peppercorns, 4 cinnamon sticks and 1 whole nutmeg pod over medium heat for 2 minutes, until fragrant. Transfer to a sealable quart jar and add 2 1/2 cups vodka, then seal and steep for 2 days, shaking the jar twice a day. Strain out the solids and transfer them to a small saucepan. Add 2 cups sugar and 1 cup water, bring to a simmer, and cook until the sugar dissolves. Let the mixture cool completely, then strain the syrup into the jar with the infused vodka, and shake to combine. Refrigerate for up to 2 weeks.